The functioning of electricity markets has experienced increasing complexityas a result of deregulation in recent years. Consequently this affects the multilateral price behaviour across regions with physical exchange of power. It has been documented elsewhere that features such aslong memory and regime switching reflecting congestion and non-congestion periods are empirically relevant and hence are features that need to be taken into account when modeling price behavior. In the present paper we further elaborate on the co-existence of long memory and regime switches by focusing on the effect that the direction of possible congestion episodes has on the price dynamics. Under non-congestion prices are identical. The direction of possible congestion is identified by the region with excess demand of power through the sign of price differences and hence three different states can be considered: Non-congestion and congestion periods with excess demand in the one or the other region. Using data from the Nordic power exchange, Nord Pool, we find that the price dynamicsand long memory features of the price series generally are rather differentacross the different states. Also, there is evidence of fractional cointegrationat some grid points when conditioning on the states.