The nucleation and growth of surface clusters are described by means o
f the following approach. The growth process is divided into three sta
ges: undercritical, near-critical and overcritical stages. For each st
age, certain assumptions are made and the solutions obtained are then
joined together at the boundaries. Within the undercritical region, th
e distribution of nuclei is considered to be of an equilibrium nature,
while within the near-critical region the distribution is quasi-stati
onary. For the overcritical region the decay of clusters is considered
to be negligible. Using certain approximations for the nucleation rat
e and stable cluster growth rate, the set of equations of condensation
kinetics is solved analytically. The time dependence of supersaturati
on, nucleation rate, surface density of islands and cluster size distr
ibution are found.