We present an algorithm for computing the Hausdorff distance between two parametric curves in $mathbb{R}^n$, or more generally between two sets of parametric curves in $mathbb{R}^n$. During repeated subdivision of the parameter space, we prune subintervals that cannot contain an optimal point. Typically, our algorithm costs O(logM) operations, compared with O(M) operations for a direct, brute-force method, to achieve an accuracy of $O(M^{-1})$.