West Yorkshire Police said Grace Newton, 18, from Pontefract and Tyler Oldroyd, 17, from Ossett have been reported missing.
A force spokesperson said: “Grace is described as a white female with pink hair believed to be wearing a pink and black puffa coat.
“Tyler is described as a white male, 5ft 2inches tall, with slight stubble, wearing a blue and grey Mckenzie top, black body warmer, black coat, black jogging bottoms and black Puma trainers with white markings.”
Police and their families are concerned for their welfare.
The two are said by police to be using the train network to get around and they have connections to the North Yorkshire area, as well as Liverpool.
North Yorkshire Police appealed to the public to keep an eye out, particularly in the Whitby area.
Anyone with information is asked to contact police via 101 or use the live chat options at www.westyorkshire.police.uk/livechat quoting log 1257 of 1 August.