The total rates of the ordinary and radiative capture of stopped muons by N
i-58,Ni-60,Ni-62 nuclei have been determined. The nuclear matrix elements e
ntering into the amplitudes of muon capture by a nucleus and the excitation
energies of a final nucleus have been calculated in the quasiparticle rand
om-phase approximation. The resulting total rates of ordinary muon capture
are close to the corresponding experimental values. For the first time, rad
iative muon capture by complex nuclei has been analyzed on the basis of a m
icroscopic model of the nuclear structure, The features of charge-exchange
Gamow-Teller and spin-dipole excitations in the processes of ordinary and r
adiative muon capture by complex nuclei are discussed.