We propose and analyze a way in which effective multicomponent condens
ates can be created inside high-Q multimode cavities. In contrast to t
he situation involving several atomic species or levels, the coupling
between the various components of the dressed condensates is linear. W
e predict analytically and confirm numerically the onset of instabilit
ies in the quasiparticle excitation spectrum. [S1050-2947(98)00202-9].