A model is estimated of flows into and out of unemployment using the Johansen multivariate cointegration approach and UK data for the period 1974Q4 to 1993Q3. Two long-run equilibrium relationships are obtained (covering the outflow rate and unemployment duration) which include variables such as the replacement ratio, structural change and output. A unique feature of the model is that it allows the inflow rate to determine the outflow rate, and vice versa. This is argued to be important given the common European 'stylized' fact that inflows and outflows are both countercyclical and strongly correlated. Thus, if firms and workers are heterogeneous, hiring and firing is contemporaneous, necessitating the type of model estimated here. Some interesting results include the finding that output is not important in determining the outflow rate, and that the speed of adjustment of the outflow rate to changes in its underlying equilibrium is slow. In contrast, the proportion of long-term unemployed is positively related to output, and its speed of adjustment is relatively much faster.