We analyze the transverse instability of two-component spatial solitons in
a saturable nonlinear medium, in relation to recent experimental observatio
ns of spatial vector solitons in photorefractive media. We present the stab
ility analysis for all three realizations: dark-bright, bright-bright, and
dark-dark soliton pairs, and demonstrate that both the nonlinearity saturat
ion and incoherent mode interaction can lead to a strong suppression of the
soliton transverse instabilities. [S1063-651X(99)51708-X].