A traditional continuous Fitts' task may be described as a one-dimensional oscillation between two targets. The combination of two such oscillations along intersecting axes gives rise to a two-dimensional aiming task, allowing the study of the speed-accuracy trade-off in two-dimensional task space. In two experiments subjects were asked to draw as many ellipses as possible while passing through four targets, arranged around the extreme points of the two major axes of a model ellipse. In the first experiment, task difficulty was manipulated simultaneously along the two axes of the ellipse. Regardless of ellipse eccentricity and orientation, movement time (MT) was found to depend linearly on Fitts' index of difficulty (ID), which combines between-target distance and target width. In the second experiment, ID was manipulated independently for the short and the long axes of the ellipse. There was a strong linear relation between MT and ID averaged over the two axes, with the two independent measures of task difficulty exerting interactive effects on MT: the higher the ID on one axis, the smaller the effect of the ID on the other. The present results demonstrate that Fitts' law, only examinated so far in one-dimensional aiming tasks, generalises to two-dimensional task space.