An adaptive and iterative intertrack-interference (ITI) cancelling scheme is described for multi-track signal detection in inter-track asynchronous shingled write magnetic recording. There is write-clock frequency drift in asynchronous recording systems. Read-back signals obtained with a wide read head scanning narrow tracks thus suffer from not only intersymbol interference (ISI) but also time-variant ITI. To efficiently cope with static ISI and time-variant ITI, multi-track soft interference cancellers and two-dimensional partial-response filters are incorporated based on per-survivor processing into each trellis state defined in a one-dimensional/two-dimensional trellis-switching max-log-MAP detector. In addition, the computational complexity can be reduced based on channel interpolation and intermittent TDPR-filter control by allowing small degradation in signal detection. Computer simulation results in media-noise-dominant environments demonstrate that the proposed adaptive and iterative ITI canceller achieves bit error rates close to those obtained in a non-ITI case when the read-head off-track ratio is up to 50% in write-clock frequency difference of 0.02%.