The man who located two young boys and their father missing for more than a week in Queensland's outback says they were "pretty hungry" but in good spirits.

The father, Steven Van Lonkhuyzen, 37, and sons Timothy and Ethan, aged five and seven, disappeared while driving from Brisbane to Cairns.

After the three failed to arrive on December 16 as scheduled, police conducted extensive searches over several hundred thousand square kilometres, including areas of Miles and Taroom, through to Rolleston, much of it rugged bushland dotted with cliffs.

Steven Van Lonkhuyzen and sons Timothy and Ethan were found by a local grazier in Expedition National Park, hungry but "in good spirits". ( Supplied: Queensland Police Service )

Cattleman Tom Wagner said when he heard the trio were missing he jumped on his quad bike to start searching in Expedition National Park, north-west of Taroom in the state's central inland.

Mr Wagner, who has lived in the area for 40 years and runs 3,000 head of cattle in the park, said he knew he was onto something when he found tyre marks.

"I packed up my quad, and sandwiches and water and everything for them, and headed off and found some tracks of where they'd been about a week ago," he said.

"The tracks were pretty old in the rain, and so I knew they were in there."

He found the trio on Sunday after their car became bogged in the national park.

Mr Wagner said Mr Van Lonkhuyzen and his two boys waved him down furiously.

"They were pretty hungry - I gave them some biscuits and sandwich and that, so they woofed into those and got something in their belly," he said.

'Luckily, they stayed with their vehicle'

Mr Wagner said he was relieved the family was safe and was spared a tragedy so close to Christmas.

The trio's 4WD became bogged in an area their rescuer, Tom Wagner, described as "very easy to get lost in". ( Supplied: Queensland Police Service )

"They were really happy to see me - they were real excited, pretty well," he said.

"Luckily they stayed with their vehicle though - if they had left their vehicle, we never would have found them, probably."

Mr Wagner said "it's probably some of the roughest country around".

"A lot of sandstone cliffs - a thousand-foot high and valleys and a lot of washouts and creeks - it's very easy to get lost in," he said.

He said he had been worried about one of the boys when he found them.

"One little boy - he looked a bit sunken in the eyes and I was a bit worried about him,' he said.

"But he was still getting around all right, and they were in pretty good spirits still."