above it is now assumed that recording or reproduction is to be performed at or form the third sector of a given one of the tracks then the alternate sector address determining circuit 1 or 16 shown in fig1 or 2 is first inputted with the logical address 6 or 20 whereupon the physical address 10 or 21 is sent out in the form illustrated in fig3 at ii if a defective sector is detected before completion of the recording or reproducing operation the physical address 10 or 21 is sent out which includes as the physical sector address 28 the leading sector address of an alternate sector of the track in concern as illustrated in fig3 at iii it is pressumed that an alternate for the alternate sector itself is the sector which follows immediately after the latter when an alternate sector which is not defective is not found on the track in concern i e when a defective sector is detected where the physical address 10 or 21 is in the form illustrated at iv in fig3 a predetermined value e g the fifteenth address is placed in the least significant four bits of the physical track address 29 while the physical sector.