This paper tests the empirical validity of the Capital Asset Pricing Model (CAPM) on the Swedish stockmarket. We examine the relationship between average return and beta for common stocks listed on Stockholmsbörsen during the period 1980-2000. The method used was developed by Fama and MacBeth in 1973 to test the CAPM on the American stock market. Our findings are in line with the results presented by Fama and MacBeth, albeit generally less reliable. The hypothesis that there on a market must exist a positive tradeoff between risk and return cannot be rejected, at least not when the full testing period is considered. Our results also indicate that the relationship between beta and return is linear. Furthermore, the results show that beta is a complete measure of risk when taking the whole testing period into account. However, when analyzing the subperiods we find some deviations from the expected results as predicted by the CAPM. In spite of this, our conclusion is that the CAPM appears to have substantial empirical support on the Swedish stockmarket.