The paper presents two models of races in which there is both technological uncertainty and strategic interaction between competitors as the race unfolds. Most of the existing literature examines one or other of these features, but not the two combined. Our aim is to see how the efforts of competitors in a race vary with the intensity of rivalry between them. In our principal model, which is of a one-dimensional race, it is shown that the leader in the race makes greater efforts than the follower, and efforts increase as the gap between competitors decreases. Under certain conditions the same results hold in our second, related model, which is of a two-dimensional race.