We extend the Flory/Stockmayer gelation theory to systems consisting of N types of polymer chain in which the transition probabilities that a crosslink point on a chain of type i is connected to a chain of type j is explicitly given by p(ij) A general formula for the weight-average molecular weight is developed. Gelation is predicted to occur when the largest eigenvalue of the transition matrix Q defined in the text reaches unity. In addition to the N-component systems, the present theory can be used to elucidate the non-random crosslinking reactions where the expected crosslinking density of the primary chains is different due to the residence time distribution or the history-dependent crosslinking reactions. For the prediction of the full molecular weight distribution, a Monte Carlo simulation method is used to illustrate the resulting distribution profiles.