We present a local as well a semilocal convergence analysis of secant-like methods under g eneral conditions in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The new conditions are more flexible than in earlier studies. This way we expand the applicability of these methods, since the new convergence conditions are weaker. Moreover, these advantages are obtained under the same conditions as in earlier studies. Numerical examples are also provided in this study, where our results compare favorably to earlier ones.