Continuos credibility effects are incorporated into a simple model of optimal monetary policy. The resulting model provides explanations for a number of folk theorems about credibility in monetary policy. A central bank with low initial credibility pursues a more restrictive policy than a central bank with high initial credibility. It accommodates shocks less and expected inflation more. The higher initial credibility is, the larger is the scope for stabilisation of shocks. Calibrations show that the time consistent inflation rate is drastically reduced when the central bank takes credibility into account.