The problem of scheduling tasks with deadlines and linear loss functions was discussed in some detail in two papers [McNaughton, R. Scheduling with deadlines and loss functions. Management Sci. 6(1) 1–12; Schild, A., I. J. Fredman. On scheduling tasks with associated linear loss functions. Management Sci. 7(3) 280–285] by Robert McNaughton and the authors. In this paper, the problem of scheduling with nonlinear loss functions is attacked. In particular, certain criteria will be established for quadratic loss functions and an algorithm is proposed which will yield an optimal scheduling—i.e., a minimal total loss—for nonlinear loss functions in general.