  We have developed a new stellar population synthesis model designed to study
early-type galaxies. It provides optical and near-infrared colors, and line
indices for 25 absorption lines. It can synthesize single age, single
metallicity stellar populations or follow the galaxy through its evolution from
an initial gas cloud to the present time. The model incorporates the new
isochrones of the Padova group and the latest stellar spectral libraries. The
model has been extensively compared with previous ones in the literature to
establish its accuracy as well as the accuracy of this kind of models in
general.
  Using the evolutionary version of the model we find that we cannot fit the
most metal-rich elliptical galaxies if we keep the IMF constant and do not
allow infall of gas. We do however reproduce the results of Arimoto \& Yoshii
(1986) for the evolution of the gas, and produce colors, and, for the first
time with this type of models, absorption line-strengths. It is in fact
possible to fit the data for the elliptical galaxies by varying the IMF with
time. Our numerical model is in good broad agreement with the analytical
'simple model'. In the present paper we describe the model, and compare a few
key observables with new data for three early-type {\em standard} galaxies.
However the data, as well as our fits, will be discussed in much more detail in
a second paper (Vazdekis {\it et al.} 1996), where some conclusions will be
drawn about elliptical galaxies on the basis of this model.
