Three resonant peaks l(ν) of dislocation paths, appearing in NaCl crystals under simultaneous exposure to the Earth's magnetic field B_Earth and an ac pump field B have been observed in the radio-frequency range (ν ~ 1 MHz). Each peak corresponds to a specific experimental geometry. Resonance frequencies correspond to ordinary EPR conditions in which, however, instead of the total Earth's field, its projections onto particular crystallographic directions play part. These directions are probably related to orientations of magnetic moments at impurity centers in dislocation cores. A physical model describing well the positions all three EPR peaks l(ν) is proposed. The peak height l_m is proportional to the squared amplitude of the pump field and the time t of sample exposure to crossed fields: l_m α B²_mt The threshold amplitude B^th_m ~ 1μ of the pump field is detected, below which the effect rapidly disappears. The time of spin-lattice relaxation of radical pairs on dislocations is estimated by the threshold field B^th_m level.