Patrick Gavin, 21 from Morecambe, is wanted in connection with an assault in the town on March 31.
A woman was pulled to the ground before being kicked repeatedly.
Jamie Heap, 30, from Blackpool, is also wanted following an assault in Blackpool on April 11.
Officers said a woman was grabbed around the neck and scratched in the face.
If you can help, call 101 or email [email protected] quoting log 0726 of April 28.