New grids of stellar evolutionary models are presented for a wide range of initial hydrogen content around the solar composition. These compositions are (X, Z) = (0.80, 0.02), (0.70, 0.02) and (0.60, 0.02). Recent OPAL opacities with LS coupling and Grevesse composition were adopted, and Alexander's tables were used for lower temperatures. We consider models with core overshooting with α_ov_=0.20, and mixing length parameter l/H_p_=1.52 that seems to represent well double-lined eclipsing binary stars. Mass loss during the main sequence and in the red giant phase were taken into account. The nuclear network treats 14 isotopes and optionally the lithium burning to study its depletion in less massive models during pre main sequence evolution. The mass range covered goes from 1 up to 40Msun _ and the more massive models were followed until helium burning. The main aim of the present series of papers is, besides the inclusion of the new opacities, to explore the effects on different outputs of the stellar models, of a change of the helium content at a given metallicity. We also present isochrones in the plane logg-logM which are very useful to compare the best parameters known for binary stars (masses and radii) with theoretical predictions. The internal structure constants for apsidal motion investigations are also presented.