We extend to non deterministic recursive program schemes the methods and results which permit definition of the semantics of such schemes in the deterministic case. Under natural hypothesis the set of finite and infinite trees generated by a scheme is proved to be the greatest fixed point of the functional mapping usually attached to this scheme.[ntroduction Several authors have been recently interested in non deterministic recursive programs [1,5,11,13,14,15,16,17].These programs are obtained by introducing a connective or which has to be interpreted operationally as giving alternatives of a choice. As in the theory of deterministic recursive programs developed in [19], we shall consider non deterministic recursive program as interpretations of what we call non deterministic recursive programs schemes having the form {#'i = ~'i/1 < i < k} where each ~' i is a term built up from constant function symbols, unknown function symbols ~,; and the binary symbol or. It is clear that every non deterministic reeursive program can be obtained from such schemes by interpreting the constant function symbols.Our aim in this paper is to define the one'many function computed by a non deterministic reeursive program scheme under the Herbrand interpretation H, including all infinite computations of the program scheme (H is the interpretation which has as domain the set of finite and infinite trees and where the *A first version of this paper was presented