Swedish DJ Avicii had a secret girlfriend and was a doting step-father to her young son at the time of his death.

Model Tereza Kačerová posted a heartbreaking open letter on her Instagram, in which she revealed that the pair had been planning on having children of their own.

She also posted a video of photographs from their time together, showing Avicii's close relationship with her son Lucas.

Avicii, whose real name was Tim Bergling, was found dead in the city of Muscat, Oman, on Friday last week.

Family: Avicii's girlfriend, model Tereza Kačerová revealed in a letter posted on Instagram that they were in a serious relationship and that Avicii was a doting step-father to her son Lucas

Secret is out: She writes that she wanted to keep their relationship private due to the 'madness' of Avicii's fame

Doting: The emotional open letter reveals that Avicii had a close relationship with Ms Kačerová's son and that they were planning to have children of their own in the future

'Dear Tim, ' Ms Kačerová writes in the letter to the late 28-year-old. 'I've spent the last days waiting to wake up, waiting for someone to tell me this is some sick joke, some awful mistake. I think it's finally settling on me now that I will truly never get to see you again'.

In her letter, she reminisces of their time together and speaks of their plans for their future.

'I used to tell you that Luka will never remember a life without you. Now I hope that he will remember his life WITH you. I'll be there to remind him. I'll show him

'Every time I think about something we won't finish I feel physical pain in my heart.

'We never finished the Harry Potter marathon - we had the last one left - you never witnessed me having a meltdown when Snape dies.

'I never finished persuading you that our daughter's name MUST be Serafina.

'You never finished your tattoo sleeve in which the inner forearm would have a face coincidentally resembling mine.'

Travels: Avicii and his girlfriend smile for the camera while on horseback

Family: The couple are posing at an unknown location while Lucas sleeps in a stroller

Happy Halloween: The pair are posing at a fancy dress party where Avicii appears not to have taken part in the theme

Adorable: This image shows the DJ teaching his step-son how to use the DJ decks

Meeting: The Czech model also posted this image, writing that it was taken on their first date

She continues: 'I was always very set on keeping our relationship private because I wanted it to be OURS and ours only and wanted no part in that madness.

'But I thought, if I'm going to share this with the world, it will be when I'm pregnant with our child. Ohhh how that plan went awry.'

I called you baby angel. Little did I know how soon you would become one.

'The last words you ever said to me were "I love you". Well I LOVE YOU. As much as you love Mexican Coke... and then some.'

Miss Kačerová is Czech-born model who grew up in Vermont, U.S. and, among other things, appeared in the video to Maroon 5's 2014 hit Maps.

True love: Another photo in the video posted on Instagram shows the pair kissing

Meet and greet: Ms Kacerova appears to have welcomed her partner at an airport with a large sign and wearing Avicii masks with a friend

Close: The model started the video with this adorable snap of Avicii and her son asleep

Adventures: The couple are seen in a lift, with Avicii holding Lucas and smiling for the camera

Tragedy: In her letter, the model writes that she has 'spent the last days waiting to wake up, waiting for someone to tell me this is some sick joke'

Sad: She writes that the couple had never had time to finish their Harry Potter film marathon

In December last year, she posted a picture of her young son and Avicii decorating a Christmas tree to her 52,700 followers, captioned 'My manz'.

Avicii's face is obstructed by his arm, and it appears the pair had gone to great lengths to keep their relationship from the public eye.

Her emotional posts follows an open letter from the Swedish DJ's family where they said the 28-year-old 'could not go on any longer and wanted peace'.

The letter, signed 'The Family', described Avicii as a 'fragile artistic soul and a sensitive guy not made for the machinery he ended up in'.

A spokeswoman for the artist declined to confirm whether he had taken his own life.

AVICII'S FAMILY'S OPEN LETTER Read the family's open letter, published on Thursday, in full below; 'Our beloved Tim was a seeker, a fragile artistic soul who always carried great existential questions. 'An overperforming perfectionist who travelled and worked hard at a tempo which led to extremely difficult stress. 'When he stopped touring, he wanted to find a balance in life to feel good and be able to do what he loved the most - music.' 'He truly battled thoughts about the Meaning, Life, Happiness. 'Now, he could not go on any more. He wanted peace. 'Tim was not made for the machinery he ended up in, he was a sensitive guy who loved his fans, but shunned the spotlight,' the statement read. 'Tim, you will forever be loved and missed. Who you were and your music will carry on the memory of you. 'We love you, the family'. Advertisement

Despite a meteoric rise to success following the release of hit-single Le7els in 2011, Avicii announced in 2016 that he would not longer perform live, following years health problems caused by stress and alcohol abuse, as well as severe anxiety.

A recent documentary, Avicii: True Stories shed light on the extreme pressure he was under, performing 320 shows in a single year.

In the documentary, Avicii, a self-confessed introvert, speaks frequently about using alcohol as a crutch to be able to perform, drinking every day during his hectic tour, and to help him with his crippling anxiety and stress.

At the age of 21 he was diagnosed with acute pancreatitis - a potentially life-threatening inflammation of the pancreas - due in part to excessive drinking.

In 2014, Bergling was again hospitalised and forced to have his gallbladder and appendix removed.

Avicii made a fortune during his short career, cashing in $28million in 2014 alone, earning $250,000 a night when playing out sold-out shows, according to GQ.

Avicii himself was less bothered about his millions, saying in 2013 that he 'noticed straight away when I started making money, that I don't need that much money'.

In 2012 he donated the entire income of his U.S. tour - more than one million dollars - to hunger relief charity Feeding America, and in 2013 he gave one million euros to Swedish aid organisation Radiohjälpen.

Struggles: In Avicii: True Stories, the DJ himself can be heard saying he is 'going to die' if he does not stop performing, and that he has told his management this 'so many times'

Breakneck speed: The 28-year-old Swedish DJ and producer retired from performing live in 2016 following a battle with alcohol abuse and anxiety

Bergling grew up in affluent Ostermalm in the Swedish capital Stockholm, and began producing music in high school.

He made a name for himself on the EDM (Electronic Dance Music) scene, before his breakthrough hit Le7els in 2011.

He would later become known for hits like Wake Me Up!, You Make Me, and recently Lonely Together, a collaboration with Rita Ora.

He won two MTV Music Awards, one Billboard Music Award and earned two Grammy nominations.

Just three days before his death, in his final post on Twitter, Bergling thanked the Billboard Music Award's jury for his nomination int the Top Dance/Electronic Album category for his EP Avīci (01).

He died on April 20 in Muscat, Oman, where he is reported to have been holidaying with friends.

The cause of death has not been made public.