Finite-dimensional Lie superalgebras G = G((0) over bar) + G((1) over
bar) over an algebraically closed field of characteristic zero, in whi
ch G((1) over bar) is a completely reducible module for the Lie algebr
a G((0) over bar), are described. In particular, the Lie superalgebras
with semisimple even part are described. (C) 1996 Academic Press, Inc
.