We have obtained radial gradients in the spectral features λ4000-Å break (D 4000 ) and Mg 2 for a sample of 11 central cluster galaxies (CCGs): 8 in clusters with cooling flows and 3 in clusters without. After careful removal of the emission lines found within the D 4000 and the Mg 2 bandpasses for some objects, the new data strongly confirm the correlations between line-strength indices and the cooling flow phenomenon found in our earlier study (Cardiel, Gorgas & Aragón-Salamanca 1995). We find that such correlations depend on the presence and characteristics of emission lines in the inner regions of the CCGs. The nuclear indices are correlated with the mass deposition rate (Ṁ ) only when emission lines are found in the central regions of the galaxies. The central D 4000 and Mg 2 indices in cooling flow galaxies without emission lines are completely consistent with the indices measured in CCGs in clusters without cooling flows. CCGs in cooling flow clusters exhibit a clear sequence in the D 4000 -Mg 2 plane, with a neat segregation depending on emission-line types (Heckman et al. 1989) and blue morphology (McNamara 1997). This sequence can be modelled, using stellar population models with a normal IMF, by a recent (∼ 0.1 Gyr old) burst of star formation, although model uncertainties do not allow us to completely discard a continuous star formation or a series of bursts over the last few Gyr. In CCGs with emission lines, the gradients in the spectral indices are flat or positive inside the emission-line regions, suggesting the presence of young stars. Outside the emission-line regions, and in cooling flow galaxies without emission lines, gradients are negative and consistent with those measured in CCGs in clusters without cooling flows and giant elliptical galaxies. Index gradients measured exclusively in the emission-line region correlate withṀ . Using the same population models we have estimated the radial profiles of the mass transformed into new stars. The derived profiles are remarkably parallel to the expected radial behaviour of the mass deposition rate derived from X-ray observations. Moreover, a large fraction (probably most ) of the cooling flow gas accreted into the emission-line region is converted into stars. In the light of this new data, we discuss the evolutionary sequence suggested by McNamara (1997), in which radio triggered star formation bursts take place several times during the lifetime of the cooling flow. We conclude that this scenario is consistent with the available observations.