We compute the elliptic genera of orbifolds associated with N = 2 supe
rconformal theories which admit a Landau-Ginzburg description. The ide
ntification of the elliptic genera of the macroscopic Landau-Ginzburg
orbifolds with those of the corresponding microscopic N = 2 orbifolds
further supports the conjectured identification of these theories. For
SU(N) Kazama-Suzuki models the orbifolds are associated with certain
Z(p) subgroups of the various coset factors. Based on our approach we
also conjecture the existence of ''E-type'' variants of these theories
, their elliptic genera and the corresponding Landau-Ginzburg potentia
ls.