The standard testing procedures for seasonal unit roots developed so far have been based mainly on time-invariant autoregressive integrated moving average (ARIMA) processes with AR polynomials involving seasonal differencing. One attractive alternative is to use periodic ARMA models. Convenient procedures are presented for testing for the presence of unit roots at the zero and seasonal frequencies in periodic time series. The limiting distributions are derived and tabulated simulation evidence illustrates the advantages of allowing for periodicity. The tests are illustrated via applications to macroeconomic and ozone level data.