In an earlier paper, ibid. 20, 1-20 (1984; Zbl 0534.60033), the authors studied the weak convergence of likelihood processes useful for change- point problems. Here they apply these results for studying the asymptotic behaviour of tests for the existence of a change-point and for deriving the limiting properties of estimators of change points by maximum likelihood method. They also discuss asymptotic behaviour of Bayesian estimators of change points using the invariance principle.