  We prove that time dynamics of a stochastic process of pure coagulation is
given by a time dependent Gibbs distribution if and only if rates of single
coagulations have the form $\psi(i,j)=if(j)+jf(i)$, where $f$ is an arbitrary
nonnegative function on the set of integers $\ge 1$. We also obtained a
recurrence relation for weights of these Gibbs distributions, that allowed
explicit solutions in three particular cases of the function $f$. For the three
corresponding models, we study the probability of coagulation into one giant
cluster, at time $t>0.$
