(E) e F(x, t), where F is upper semicontinuous, from known results in the theory of ordinary differential equations. This will be accomplished by showing that, for any F upper semicontinuous and convex, it is always possible to "approximate" the multivalued differential equation (E) by appropriately chosen ordinary differential equations. This would be obvious in the case of a lower semicontinuous multivalued mapping, since it is well known that in this case there exists always an ordinary differential equation whose solutions are also solutions of the given equation (E), but it is easy to see that this is not true in general for upper semicontinuous mappings. We shall investigate the properties of a certain kind of "convergence" of continuous single-valued fields to multivalued upper semicontinuous fields; we shall show that this convergence can be used analogously to the usual uniform convergence, to which it reduces when the field F is singlevalued.