Schock (1985) has considered the convergence properties of various Galerkin-like methods for the approximate solution of the operator equation of the second kindx - Tx = y, whereTis a bounded linear operator on a Banach spaceX, andxandybelong toX, and proved that the classical Galerkin method and in certain cases, the iterated Galerkin method are arbitrarily slowly convergent whereas the Kantororich method studied by him is uniformly convergent. It is the purpose of this paper to introduce a general class of approximations methods forx - Tx = ywhich includes the well-known methods of projection and the quadrature methods, and to characterize its uniform convergence, so that an arbitrarily slowly convergent method can be modified to obtain a uniformly convergent method.