The development of various approaches to describing the complete fusion of
nuclei and their connections with experimental studies is discussed. A brie
f account of the dinuclear-system concept (DNSC, the approach proposed at D
ubna, is given. The DNSC revealed two important features of the complete fu
sion of massive nuclei: the existence of the inner fusion barrier B-fus*, a
nd the competition between complete fusion and quasifission channels in a d
inuclear system formed at the capture stage. The DNSC was applied to the an
alysis of reactions used to synthesize superheavy elements (SHE). The DNSC
provided a basis for the models of competition between complete-fusion and
quasifission channels. Using these models, one can describe the cross secti
on for SHE production in cold- and warm-fusion reactions. (C) 2001 MAIK "Na
uka/Interperiodica".