Possible existence of deeply-bound nuclear states ofK¯is investigated theoretically for few-body systems. The nuclear ground states ofK¯in3Heand4Heare predicted to be discrete states with binding energies of 108 MeV and of 86 MeV and widths of 20 MeV and of 34 MeV, respectively. The formation of theT=0 K−⊗3He+K¯0⊗3Hstate in the4He(stoppedK−,n) reaction is proposed with a calculated branching ratio of about 2&percent;. It is discussed that a kaon injected into9Beforms a nuclear object of very high density and low temperature. ©2001 American Institute of Physics.