In this paper, we introduce a rather straightforward but fundamental observation concerning the convergence of the general iteration process. x^(k+1) = x^k - alpha(x^k) [B(x^k)]^(-1) grad­f(x^k) for minimizing a function f(x). We give necessary and sufficient conditions for a stationary point of f(x) to be a point of strong attraction of the iteration process. We will discuss various ramifications of this fundamental result, particularly for nonlinear least squares problems.