Abstract:It's well-known since the work of Y.Ruan and T.Milanov, that the mirror of a LG B--model defined by a simple--elliptic singularity is an elliptic orbifold. This result was further extended by Milanov and Shen who established the LG--LG type isomorphisms for the simple--elliptic singularities. In this talk we will discuss in details the A and B models of the simple--elliptic singularities with the nonmaximal/nontrivial symmetry groups.