Cool cat … Louise Booth and Fraser with Billy. Credit:Cristian Barnett © Hodder & Stoughton For the past 18 months, Fraser had been receiving treatment from a small team of experts, including a speech therapist and a behavioural therapist. We'd been told that he would never attend a normal school, but we managed to find a small, private nursery to take him twice a week. The less good news was that his moods and behaviour were still highly unpredictable and volatile. This meant that our lives were never straightforward. Fraser is a loving little boy with a personality that melts the hearts of everyone who meets him. But I'd be lying if I said our life together was a bed of roses. We never quite knew what to expect nor what to do, especially if we changed routine, as we'd done today. All we could do was follow our instincts. Which was why Chris and I were driving to meet the local organiser for a cat charity. Our family's only pet at the moment was a cat, a rather portly and ageing grey called Toby. For most of his young life, Fraser had taken very little interest in his surroundings, or Toby. He was obsessed with anything that had wheels or spun around, and could spend hours watching a spinning washing machine, playing with an old DVD player or whirling the wheels of his up-ended buggy or a toy car, but beyond that very little seemed to engage him. Recently, however, I'd noticed that he'd become fascinated by Toby. He'd lie alongside Toby, placing his head on the carpet so that he could stroke and try to communicate with him. Toby hadn't reciprocated the interest. This didn't really surprise me. I knew that Toby wasn't a pet for a young child, but Fraser's behaviour had set me thinking. I sent an email to Cats Protection, explaining that we were looking for a "special" animal to be his friend. That was exactly the way I worded it, a "special" friend. I had no great expectation of such a creature even existing.

I was soon contacted by the organiser, a lady called Liz. I could tell immediately that she understood what I was looking for. "I've got a couple of cats that would be suitable. But I have a feeling I know which one you will go for," she said. I received an email with a photo of two identical-looking cats, Billy and Bear. They were both grey, with white markings on their faces and bellies. I ran off a couple of matchbox-sized prints of Bear and Billy so that Fraser could see his potential new friends. He'd taken the pictures to bed with him each night and spent hours studying them. Goodness knows what thoughts went through his mind as he lay there, poring over the prints of these identical cats. I say identical, but the interesting thing was that he could tell the difference between them. To my eyes, they were so similar that I had to write their names on the back of the pieces of paper to distinguish them. But Fraser knew which was which and repeatedly explained that "this is Billy and this is Bear". Autism has so many quirks to it - Fraser could barely walk and couldn't communicate properly, but he could tell the difference between these two doppelgänger cats. After a week of preparation, I was fairly confident Fraser understood what was about to happen. We were going to see these two cats and, if we liked them, one of them would come to live with us. Billy had sussed out in two days what it had taken us the best part of two years to work out.

Sitting in the car, my mind was racing. There was nothing unusual in that. There were times when I wondered whether I had turned into the world's most neurotic mother. But the truth of the matter was that as the parent of an autistic child, I constantly had something to be anxious about. What if he was frightened by Liz? What if he didn't like the look of her house? What if he was upset by a noise in the house? What if he didn't like the cats? At the house, there was a raised platform where the two cats were lying down. One was half asleep and was facing in the other direction but the other one was sitting bolt upright, looking intrigued at the new arrivals. "This is Bear," Liz explained, pointing at the disinterested one. "And this is Billy." At that precise moment, the second cat sprang on to Liz's shoulder. He then jumped off and went straight to where Fraser was standing. Fraser didn't flinch - quite the opposite. He stood there smiling, fascinated. "Would you like to come in and say hello to Billy, Fraser?" Liz asked. "Yes," he said. "Mummy, will you come with me?" Chris and I exchanged a look that spoke volumes. For other parents this might have seemed like nothing but to us, the parents of a boy who had spent the previous three years being frightened of everything, it was very exciting. What happened next, however, was beyond exciting. To me, it was mind-blowing. Inside the pen, Fraser immediately sat on the floor. Before I knew it, Billy had strolled straight over and plonked himself on top of him, landing on his chest. Normally, I would have expected a bellowing scream. There was no noise, no bad reaction. Nothing.

Instinctively, Billy seemed to sense that Fraser wasn't quite comfortable, so he slid off his chest and adjusted his position so that his body weight wasn't pressing on him any more, just his front paws. He then extended his neck as far it could go so that he could nuzzle his head close to Fraser's. The pair then sat there, cuddling each other quietly, as if there was no one else in the world. "It looks like Billy has already chosen you," Liz said. I sensed that Billy had an instinctive understanding of Fraser and his needs. For instance, Fraser loved to lie on the floor to watch TV. Billy cottoned on to this and would position himself within touching distance. Fraser always responded. He'd place his head on Billy's belly or curl up next to him. On a couple of occasions I sat in the room with them, sipping a cup of tea as I watched them interacting. One of the things that struck me early on was how, while they were rolling around on the rug, Billy would lean into Fraser, pressing his forehead into his chest as if he was head-butting him. Often he'd do this while Fraser was lying on his back, almost pushing him down into the floor. He seemed to know that Fraser liked this. How? I had no idea. It was only when Fraser was properly diagnosed with hypotonia that it was explained to us that he needed to feel solidity around him. So he lay on his back in order to get a feeling of contact, pressure, on his spine and on his legs. Any other position left him feeling unsupported and, therefore, insecure. Billy had sussed out in two days what it had taken us the best part of two years to work out. He was applying pressure because, somehow, he knew Fraser needed it.

"They're like peas in a pod, those two," I told Chris over dinner one evening. "I think Billy understands him better than we do." "We'll see," Chris said with an arch of his eyebrow. "Let's see if he understands him when he's having a meltdown." It was a fair point. Bathing Fraser had always been a problem. I have a picture of his first bath and you'd think he'd been placed in boiling water. He was completely red but it wasn't from the heat, it was from screaming. If giving him a bath was hard, washing his hair was even worse. He hated it more than he hated anything in the world and, in Fraser's case, that was saying rather a lot. One night, Chris and I braced ourselves for the ordeal. We'd managed to get Fraser into the bath, but pandemonium had broken out. He had turned bright red and was screaming "No, no, no!" and "Don't touch my hair!", covering his head with his hands. Chris and I knew the signs well enough.

It was so bad that we were facing a real mother of all meltdowns, an 11 out of 10. "This is pointless," Chris said, exasperated after five minutes of bedlam. "We aren't going to get anywhere tonight. I think we might as well get him out." I was inclined to agree. Apart from anything else, I thought our new neighbours might call the police because it must have sounded as if we were murdering a child. I was about to reach for Fraser's towel and start getting him out when I sensed an unexpected presence in the bathroom. Billy. "What are you doing in here?" Chris said. We were still holding a flailing Fraser in the water but we slid over to give Billy some space and watched in mild disbelief as he lifted himself up and proceeded to put both paws on the edge of the bath. He then stretched himself to his full height and leaned as far as he could over the water so he could push his face as close as possible to Fraser. He was soon soaked to the skin. At one point, Fraser flicked some of the bubble bath in his face and he had to wipe it away with his paw. But Billy remained fixed to the spot until Fraser started to calm down.

"Look, Billy doesn't mind getting his hair wet, so why don't you let me wet yours?" Chris said, sensing an opportunity. Fraser didn't say anything, which, for us at least, was tantamount to a yes. Chris gently rubbed shampoo into Fraser's head and worked it into a lather as I, quietly, got ready to rinse it out. This was the bit Fraser hated the most. Ordinarily, it would have meant the outbreak of World War III. But on this occasion he let me gently wash out the soap. In fact, he went one step further and leant his head back to help the process. If I'd been more religious, I'd have considered singing "Hallelujah!" Edited extract from When Fraser Met Billy by Louise Booth, published by Hachette Australia.