It is shown that an infinite-dimensional dynamical system of the form $$\begin{gathered} 2\left( {t + to} \right)\left( {\beta _1 \dot \beta _1 + r_1 (\beta )\dot \beta } \right) = \left( { - \beta _1^2 + 2\sum\limits_{j \geqslant 2} {\beta _j^2 } } \right) + s_1 (\beta ), \hfill \\ 2\left( {t + to} \right)\left( {\dot \beta _k + R_k (\beta )\dot \beta } \right) = \left( {k + 2} \right)\beta _k + s_k (\beta ),k \geqslant 2, \hfill \\ \end{gathered} $$ studied for sufficiently small r 1, s 1, R k , and S k in the preceding part of this work [Contemporary Mathematics and Its Applications, Vol. 2. Partial Differential Equations (2003), pp. 22–49] describes the evolution of the free boundary in the problem of the Hele-Shaw flow in the case where the pressure is constant on the free boundary (Leibenson condition).