We present the results of a morphological analysis of a small subset of the SWIRE galaxy population. Our analysis is based on public ACS data taken inside the SWIRE N1 field. We distinguish two very general classes of galaxies, bulge- and disc-dominated galaxies, the first class being referred to with the general term 'spheroids' and the second containing everything from spirals to irregulars and pairs. Even though the requirement for 3.6- and/or 4.5-micron detections favours the selection of early-type galaxies, the observations show that the large majority (close to 80 per cent) of the 3.6- and 4.5-micron galaxy population, even at these moderately faint fluxes, is dominated by spiral and irregular galaxies or mergers, already suggesting that elliptical galaxies assemble late. We then limit our sample to objects with IRAC fluxes brighter than 10 microJy, estimated ˜ 90 per cent completeness limit of the SWIRE catalogs, and compare the observed counts to model predictions. The observed 3.6- and 4.5-micron early-type counts are in very good agreement with the estimations of the hierarchical scenario, showing however a deficit toward the faint end, possibly reflecting some incompleteness that is already introduced at this flux level. The monolithic predictions imply steeper counts and fail in reproducing the observations.