We have undertaken a study of the nature of red galaxies at low and intermediate redshifts in the GOYA photometric survey. A new photometric index based on apparent magnitudes has been obtained to separate red galaxies dominated by old populations from those dominated by star formation. A two-component mass code has been used to estimate the stellar mass and age of the galaxies. The main results are: the two types of galaxy have differences in their masses, age and number densities; the red galaxies at z < 1 with masses greater than 1011M&sun; are passive; the bulk of the passive galaxies at 0.3 < z < 1.5 had their last starburst between 1 < z < 2; the number density of the passive galaxies decreases while that of the dusty star-forming galaxies increases in the redshift range 0.3 < z < 1.5. All these results are compatible with a scenario in which the dusty star-forming galaxies are transitional galaxies between the blue and passive galaxies.