Starting with the kinetic equation for the distribution function in th
e phase-space of a nucleon, a closed set of equations is obtained desc
ribing in a classical way the process of fusion. This is achieved usin
g the generalized virial theorems and by making simplifying assumption
s of the following nature: (i) restrictions are imposed on the shapes
of composite systems and the collective flow of the nuclear matter ins
ide them; (ii) the nuclear mean field is assumed at each moment to be
the same as in the equilibrated nuclear matter; (iii) the collective m
otion energy dissipation is described through a collision term issuing
from a mean-relaxation-time approximation. The theory is prepared for
the application to study the fusion of two identical spherical nuclei
experiencing the head-on collision. It shows in particular that the F
ermi-surface deformation affects both the force driving the system to
the equilibrium and its dissipative properties.