Seasonal patterns in economic time series are generally examined from a univariate point of view. Using extensions of the unit root literature, important classes of seasonal processes are deterministic, stationary stochastic or mean reverting, and unit root stochastic. Time series tests have been developed for each of these.This paper examines seasonality in a multivariate context. Systems of economic variables can have trends, cycles and unit roots as well as the various types of seasonality. Restrictions such as cointegration and common cycles are here applied also to examine multivariate seasonal behaviour of economic variables. If each of a collection of series has a certain type of seasonality but a linear combination of these series can be found without seasonality, then the seasonal is said to be ‘common’. New tests are developed to determine if seasonal characteristics are common to a set of time series. These tests can be employed in the presence of various other time series structures.The analysis is applied to OECD data on unemployment for the period 1975.1 to 1993.4, and it is found that four diverse countries (Australia, Canada, Japan and USA) not only have common trends in their unemployment, but also have common deterministic seasonal features and a common cycle/stochastic seasonal feature. Such a collection of characteristics were not found in other groups of OECD countries.