In this paper, finite travelling waves for the semilinear parabolic systems «n = d,u", ~ e 'Tl"""• ' = ' " (*) are studied, where i, > 0, e, > 0, m" > 0 for all 1 < i,j < n, and 5Z"=i m u > 0 *°r a " ' 5 ' 5 "• Let M = (m,j) nxn and A = I -M. It will be proved that (*) has finite travelling waves if and only if all principal minors of A are positive. Moreover, some asymptotic behaviours of finite travelling waves will be obtained.