Derivative-free nonlinear least squares algorithms which make efficient use of function evaluations are important for fitting models defined by systems of nonlinear differential equations. A new Gauss-Newton-like algorithm with these properties is developed. The performance of the new algorithm (called Dud for “doesn't use derivatives”) is evaluated on a number of standard test problems from the literature. On these problems Dud competes favorably with even the best derivative-based algorithms.