A method of reading a length of multitrack magnetic tape on which data is written on each track in the form of a succession of blocks, with each data block carrying a block marker. While data on each track is being read by a transducer, the output therefrom is monitored for detecting a possible blank on the track from the block markers. The tape is stopped, rewound, and paid off again when a possible blank is detected, in order to retry reading of the detected possible blank. If the detected possible blank is due to dust accumulation on the tape or on the transducer, data written thereon may be read during the retry. Reading is discontinued if no block marker is detected during the retry. Reading of a detected possible blank may be retried only at a starting part of each track, where dust is particularly easy to accumulate, or throughout each track.