This paper studies a dynamic model of a financial market with some large, strategic traders. These traders are risk-averse and exchange a risky asset for hedging purposes. The only private information in the model concerns their hedging demands. We find that they trade quickly and at a decreasing rate when there are many non-strategic traders in the market. Otherwise they trade slowly at an increasing and then decreasing rate. In that case the outcome is very inefficient and differs from the competitive one more than it does in static double auction models. We also find that strategic traders may be better off if their trades are known in advance.