In 2011 K. Kutnar, A. Malnič, L. Martinez and D. Marušič introduced the concept of the quasi m–Cayley graph for a positive integer m as follows. A finite simple graph X=(V,E) is quasi m–Cayley if there is a group G of automorphisms of X with the following properties: G has m+1 orbits on V, one of these orbits consists of a single vertex v, and G is semiregular on the set V\{v}. In this talk I report some results on vertex transitive quasi 2–Cayley graphs. This is a joint work with A. Hujdurović and K. Kutnar.