Every mode of a single-mode or multimode helical fibre is always leaky but, for practical purposes, can be treated as being bound with an effective cut-off wavelength. The leakage loss for each mode is quantified, showing that, for fixed core offset and source wavelength, the cut-off pitch increases with increasing mode order. The value of the cut-off pitch for each mode is in agreement with experimental measurements. © 1990 Chapman and Hall Ltd.