Since an analysis of seasonal fluctuation appeared to shed light on the nature of business cycles, testing for seasonal pattern in time series has been given considerable attention in the recent literature. It is also well-known that many economic and financial time series exhibit strong dependence - long memory property. This paper considers a number of procedures; namely Hassler's extension of Geweke and Porter-Hudaks (1983) (GPH) semi-parametric test, Robinson's (1983) (GPH) semi-parametric test, Robinson's frequency-domain score test and Silvapulle's time-domain test, in order to test for the long memory properties of quarterly time series at zero and seasonal frequencies. Very little is known about the finite sample properties of these tests. In a simulation study, we find that time-domain and semi-parametric tests generally have sizes close to the nominal level, with the latter having sizes higher than the nominal level at the semi-annual frequency. In terms of power, the time-domain score test dominates the other tests.