The question of how much gas cools in the cores of clusters of galaxies has been the focus of many, multiwavelength studies in the past 30 years. In this letter we present the first detections of the strongest atomic cooling lines, [C II], [O I] and [N I] in two strong cooling flow clusters, A1068 and A2597, using Herschel PACS. These spectra indicate that the substantial mass of cold molecular gas (>10^9 Mo) known to be present in these systems is being irradiated by intense UV radiation, most probably from young stars. The line widths of these FIR lines indicate that they share dynamics similar but not identical to other ionised and molecular gas traced by optical, near-infrared and CO lines. The relative brightness of the FIR lines compared to CO and FIR luminosity is consistent with other star-forming galaxies indicating that the properties of the molecular gas clouds in cluster cores and the stars they form are not unusual. These results provide additional evidence for a reservoir of cold gas that is fed by the cooling of gas in the cores of the most compact clusters and provide important diagnostics of the temperature and density of the dense clouds this gas resides in.