We consider a system of substances
Aj reacting according to the scheme:
Ai +
Aj +
Ak Ai+j+k, which is described by the generalized Smoluchovski equation. We discuss the existence of global solutions of this kinetic equation, and show that the total number of monomers may decrease as the result of the formation of infinite clustere (gelation) for some special coagulation kernels. We also solve the case R(i, j, κ) = s
is
js
κ with s
κ =
Ak +
B explicitly, and find that the gelation indeed occurs at t
c = (6
A +
B)/6
A2(
A +
B)
2.