It is assumed that the size distribution c_k(t) satisfies Smoluchowski's coagulation equation with rate coefficients K(i, j), behaving as K(i, j) approximately i^muj^nu (i<<j), and find the following: in gelling and nongelling systems of class I ( mu >0) the general solution c_k(t) approaches for t to infinity the exact solution Cb_k/t(k=1, 2, . . .), where the b_k's are independent of the initial conditions c_k(0), and can be determined from a recursion relation. In class II systems ( mu =0), c_k(t)/c₁(t) to b_k (t to infinity , k=1, 2, . . .), but the b_k's depend on c_k(0). Only in the scaling limit (k to infinity , s(t) to infinity with k/s(t)=finite; s(t) is the mean cluster size) does c_k(t) approach a form independent of the initial distribution. Class III, where c_k(t)/c₁(t) to infinity (t to infinity , k=2, 3, . . .), has not been considered here.