Seasonal streamflow series generally exhibit periodicity in the autocovariance structure. Such periodicity can be represented by PARMA models, i.e., autoregressive moving average (ARMA) models with parameters that vary with the seasons. Statistical properties of low-order models such as the PARMA (2,2) model are examined. The periodic moment equations are derived; they can be used to compute the periodic covariance structure of a given model. Simulation of streamflow at several sites can be done using the contemporaneous PARMA model. The main problem in using such models is to determine the covariance matrices of innovations. Traditionally, this has been done by the method of maximum likelihood. However, this method generally leads to significant underestimation of the cross correlation of flows. A moment estimator is developed herein for the contemporaneous PARMA(2,2) model along with three approximate moment-based estimators for those cases where a feasible moment solution cannot be obtained. The applicability of the proposed methods is illustrated by fitting PARMA models to weekly flow data for two catchments in the Ottawa River basin. ¿ American Geophysical Union 1996