Marshall-Olkin exponential distribution has been studied by Salah, et, al. (2008). In this paper, we derive several recurrence relations satisfied by the single moments and product moments of progressive type-II censored order statistics from Marshall-Olkin exponential distribution. These relations may then be used to compute all means, variances and covariances of progressive type-II censored ordered statistics based on Marshall-Olkin exponential distribution for arbitrary censoring scheme.