We have analyzed the Percus-Yevick (PY) and the mean spherical model (MSM) equation for an N-component system of sticky hard spheres. The PY approximation leads to a set of N(N + 1)/2 coupled quadratic equations for the unknown coefficients. While for this closure, the pair distribution functions have to be calculated numerically, we can proceed in the MSM one step further if we assume a Lorentz-Berthelot-type rule for the interactions: then the structure functions can be calculated analytically. We show that under these conditions in;the limit N-->infinity (stochastic limit) the analyticity of the solution is preserved. General expressions both for the discrete and continuous (polydisperse) case are presented.