We have considered coagulation processes containing n-polymer interactions by means of a generalized Smoluchovski's equation, which is solved as a monodisperseinitial-value problem to the kernel: K(i1,i2,…,in)=A sumfrom i=1 to n i1+B, K(i1,i2,…,in)=A sumfrom i=1 to n i1. According to the connection between model K(i1,i2,…,in)=A sumfrom i=1 to n i1+B and K(i1,i2,…,in)= S(i1)S(i2)…S(in)(S=Ak+B),we obtain the pre-gel solution of the latter model. We also study a kind of joint coagulation process containing two-polymer and three-polymer collisions with the kernel K2(i, j)=i+j and K3(i,j,k) = i+j+k and get the explicit expression of Cm(t). Finally, we discuss the long-term behavior of Cm(t), Which can be extented to the general case.