A general expression has been obtained for the polarisation of an assembly of two-level systems irradiated by a sequence of N radiation pulses. The times and amplitudes of the echo-polarisation have been obtained. The method is an extension of the T-matrix method for the exact solution of the problem of interaction of radiation with two-level systems. The number of polarisation echoes is 3^N−1−N. The echo times are given by$$t' = (1 + a)t_N + (b - a)t_{N - 1} + (c - b)t_{N - 2} + \cdots + (q - p)t_1 $$ wheret_k are the pulse times anda, b, c take on values 1, 0, − 1. From the general expression the amplitudes of echoes due to sequences of 2, 3 and 4 pulses are obtained as special cases. Distinct echo sequences determined by time relations among the incident pulses are discussed. The echo sequences exhibit interesting features which are of significance in the application of the phenomenon in holophony, etc.