There is a large class of equations containing a small parameter whose solution as the parameter tends to zero converges only weakly in certain portions of space-time. Because of nonlinearity these weak limits do not satisfy the equation obtained by setting the parameter equal zero. Examples where the limits can be described are the Korteveg-de Vries equation, the classical limit of the cubic Schroedinger equation, and the Toda lattice. The presentation will be expository.