Superconductivity in two-band models involving non s-wave pairing is i
nvestigated. We consider the following case: one band has s-wave pairi
ng interaction and the other has non s-wave pairing interaction, and o
nly s-wave Cooper pairs can be transferred between bands. Possible app
earance of non s-wave superconducting order parameter in an s-wave sup
erconducting state and its onset temperature are discussed. The non s-
wave order parameter is suppressed by s-wave superconductivity, and ca
nnot appear unless the non s-wave pairing interaction is stronger than
critical value. We also consider the appearance of s-wave superconduc
ting order parameter in a non s-wave superconducting state. In this ca
se, the s-wave order parameter can always appear on lowering temperatu
re. Temperature dependence of the order parameters and the specific he
at are shown in a simple case.