We suggest a simple asset market model in which we analyze competitive and strategic behaviornsimultaneously. If for competitive behavior two-fund separation holds across periods then itnalso holds for strategic behavior. In this case the relative prices of the assets do not dependnon whether agents behave strategically or competitively. Those agents acting strategically willnhowever invest less in the common mutual fund. Constant relative risk aversion and absencenof aggregate risk are shown to be two alternative sufficient conditions for two-period fundnseparation. With derivatives further strategic aspects arise and strategic behavior is distinctnfrom competitive behavior even for those utility functions leading to two-fund separation.