Non-l,~cal charges are defined as a natural generalization of standard charges in relativistic quantum field theory. The general form of a non-local charge in terms of asymptotic fields is given and preliminary results on the restrictions imposed on non-local charges in interacting theories are reported [8]. 1. Recently Lfischer [1 ] established the existence of a new type of constants of motion in the quantum non-linear o-model in two space-time dimensions. He proved that in this model the operators .ha are conserved quantities, i.e. they commute with the time translations. Here j~t b = -1 # a,b = 1 .... n are currents which can be derived from the O(n)-symmetry of the model and Z is a renormalization constant. The novel feature of these 'non-local charges' is that they are obtained by multiple integration of products of local fields. As a result the operators Qab have some interesting properties which are not shared by the standard charges. It turns out, for example, that Qab does not commute with the S-matrix, thereby providing a direct and elegant proof that there is interaction in the non-linear o-model. It was also stated in [1 ] that the restrictions arising from the existence of the charges Qab exclude particle production and are consistent with the factorization of the multiparticle S-matrix into products of two-particle S-matrices. The latter fact would make it possible to calculate the S-matrix exactly [2]. In view of this example it is worthwhile to find out what can be said about non-local charges in the general setting of local quantum field theory. In particular it is desirable to extend the discussion of non-local charges to higher dimensions of space-time. At first sight such a program might seem to be hopeless for two reasons. First, the existence of non-local charges depends on non-linear relations between local fields, in contrast to the linear relation Ouju = 0 in * On leave of absence from the