The possibility of creating a Bose condensate of trapped atoms in a no
n-ground-state is suggested. Such a nonequilibrium Bose condensate can
be formed if one first obtains the conventional Bose condensate in th
e ground state and then transfers the condensed atoms to a non-ground-
state by means of a resonance pumping. The properties of ground and no
n-ground-states are compared and plausible applications of such nonequ
ilibrium condensates are discussed. [S1050-2947(97)03912-7].