Аннотация:We propose a new approach for studying the neutron star/supernova remnant associations, based on the idea that the supernova remnants (SNRs) can be products of an off-centered supernova (SN) explosion in a preexisting bubble created by the wind of a moving massive star. A cavity SN explosion of a moving star results in a considerable offset of the neutron star (NS) birth-place from the geometrical center of the SNR. Therefore: a) the high transverse velocities inferred for a number of NSs through their association with SNRs can be reduced; b) the proper motion vector of a NS should not necessarily point away from the geometrical center of the associated SNR. Taking into account these two facts allow us to enlarge the circle of possible NS/SNR associations, and could significantly affect the results of previous studies of associations. The possibilities of our approach are illustrated with some examples. We also show that the concept of an off-centered cavity SN explosion could be used to explain the peculiar structures of a number of SNRs and for searches for stellar remnants possibly associated with them.