A new reaction kernel, K(j, k) = 2-q(j)-q(k) with 0 < q < 1, is introduced,
for which the Smoluchowski equations of aggregation (c)over dot(j) = 1/2 S
igma(k,l=1)(infinity) K(k, l)c(k)c(l)[delta(k+l,j)-delta(k,j)-delta(l,j)] c
an be solved. The time evolution of the concentrations c(j)(t) and of their
moments M-n(t) = Sigma(j=1)(infinity) j(n)c(j)(t) is analysed. The c(j)(t)
decay at large times as t(-(2-qj)) in striking contrast to the behaviour o
f the constant kernel K(j, k) = 2, for which c(j)(t) behaves as t(-2) at la
rge times. On the other hand, the moments behave in leading order at large
times exactly like the moments of the constant kernel, though differences a
ppear at higher orders.