The assumption of linearity is tested using five statistical tests for the US and the Canadian unemployment rates and the employment sectoral shares growth rates; construction, finance, manufacturing and trade. An AR(p) model was used to remove any linear structure from the series. Evidence of non-linearity is found for the sectoral shares with all five statistical tests in the US case but not in the aggregate level. The results for Canada are not so clear-cut. Evidence of unspecified non-linearity is found in the unemployment rate and in the sectoral shares. Overall important asymmetries are found in disaggregated labour market variables in the univariate setting. The linearity hypothesis was also examined in a multivariate framework. Evidence is provided that important asymmetries exist and a linear VAR cannot capture the dynamics of employment reallocation.