ABSTRACT. It is natural to ask whether one can extend the notion of a Haar subspace so as to be valid in an arbitrary normed linear space, and at the same time preserve as much of the C[a, b]-theory as possible. In this paper we introduce the notion of an interpolating subspace of a normed linear space. In the particular space C(T), T compact Hausdorff, the interpolating subspaces turn out to be precisely the Haar subspaces. (Recall that an n-dimensional subspace M of C(T) is called a Haar subspace if every function in M \ {0} has at most n − 1 zeros in T.) We shall verify that corresponding to each one of the classical results which hold for Haar subspaces in C[a, b], there is a strictly analogous result valid for interpolating subspaces in an arbitrary normed linear space.