We present a detailed analysis of the X-ray properties of the cooling flows in a sample of nearby , X-ray bright clusters of galaxies using high-quality ASCA spectra and ROSAT X-ray images . We demonstrate the need for multiphase models to consistently explain the spectral and imaging X-ray data for the clusters . The mass deposition rates of the cooling flows , independently determined from the ASCA spectra and ROSAT images , exhibit reasonable agreement . We confirm the presence of intrinsic X-ray absorption in the clusters using a variety of spectral models . We also report detections of extended 100 \mu m infrared emission , spatially coincident with the cooling flows , in several of the systems studied . The observed infrared fluxes and flux limits are in good agreement with the predicted values due to reprocessed X-ray emission from the cooling flows . We present precise measurements of the abundances of iron , magnesium , silicon and sulphur in the central regions of the Virgo and Centaurus clusters . Our results firmly favour models in which a high mass fraction ( 70 - 80 per cent ) of the iron in the X-ray gas in these regions is due to Type Ia supernovae . Finally , we present a series of methods which may be used to measure the ages of cooling flows from the X-ray data . The results for the present sample of clusters indicate ages of between 2.5 and 7 Gyr . If the ages of cooling flows are primarily set by subcluster merger events , then our results suggest that in the largest clusters , mergers with subclusters with masses of \sim 30 per cent of the final cluster mass are likely to disrupt cooling flows .