Summary Progressive censoring schemes (allowing a continuous monitoring of experimentation until a terminal decision is reached) are often adopted in clinical trials and life testing problems. In this paper, a general class of rank order tests for progressive censoring is proposed. Along with a basic martinga:le property and a Brownian motion approximation for a related rank order process, asymptotic distribution theory of the proposed statistics is developed. Asymptotic performance characteristics of the proposed tests (in the light of Bahadur efficiency and the stochastic smallness of the stopping variables) are studied.