A number of methods for cancelling magnetoacoustic and piezoelectric ringing signals in the spectroscopy of the nuclear quadrupole resonance are presented. The suggested methods include using the sequence (q~0)~-(z-~p~-2z'-q~v-2"r-~o_,-2z-~p_v-z) . anda multipulse analog of the twopulse Hahn sequence with the first pulse replaced by a short steady-state sequence. Another method presented is the method of orthogonal effective fields for a fast saturation of the quadrupole spin system which can be used for subtracting the magnetoacoustic and piezoelectric components from the signal. The suggested methods can be used for the practi~:al purposes of detecting explosive substances and narcotics.