We consider a model for bilayer superconductors where an interlayer pa
iring amplitude Delta(perpendicular to) coexists with intralayer pairi
ng Delta(parallel to) of d(x2-y2) symmetry. This model is motivated by
a recent photoemission experiment reporting the splitting of the node
s of the energy gap. In addition to offering a natural explanation of
this observation, the model has a number of new experimental consequen
ces. We find that the new state is accompanied by a spontaneous breaki
ng of the tetragonal symmetry. We also find that the out-of-phase osci
llation of Delta(perpendicular to) and Delta(parallel to) gives rise t
o a new Raman active mode. The phase of Delta(perpendicular to) may al
so become imaginary, leading to a state which breaks time reversal sym
metry, which may have important implications for tunnelling experiment
s.