We consider a model for bilayer superconductors where an interlayer pa
iring amplitude Delta(perpendicular to), coexists with intralayer pair
ing Delta(parallel to) of d(x)2(-y)2 symmetry. This model is motivated
by a recent photoemission experiment reporting the splitting of the n
odes of the energy gap. In addition to offering a natural explanation
of this observation, the model has a number of new experimental conseq
uences We find that the new state is accompanied by a spontaneous brea
king of the tetragonal symmetry. We also find that the out-of-phase os
cillation of Delta(perpendicular to) and Delta(parallel to) gives rise
to a new Raman active mode. The phase of Delta(perpendicular to) may
also become imaginary, leading to a state which breaks time reversal s
ymmetry, which may have important implications for tunnelling experime
nts.