A regime dependent VAR model is suggested that allows long memory (fractional integration) in each of the regime states as well as the possibility of fractional cointegra- tion. The model is relevant in describing the price dynamics of electricity prices where the transmission of power is subject to occasional congestion periods. For a system of bilat- eral prices non-congestion means that electricity prices are identical whereas congestion makes prices depart. Hence, the joint price dynamics implies switching between essen- tially a univariate price process under non-congestion and a bivariate price process under congestion. At the same time it is an empirical regularity that electricity prices tend to show a high degree of fractional integration, and thus that prices may be fractionally cointegrated. An empirical analysis using Nord Pool data shows that even though the prices strongly co-move under non-congestion, the prices are not, in general, fractional cointegrated in the congestion state.