We propose to use ISO observations of infrared fine structure lines to measure the amounts of line-emitting gas at the centers of cooling-flow clusters, the depletions of refractory elements in this gas, and the hardness of the photoionizing spectrum that fuels the line emission. If clusters contain additional X-ray absorbing cold gas extending to 100 kpc radii, our observing program will allow us to study this gas as well. The clusters we wish to observe (Autumn launch: Abell 1795 and Abell 2597; Spring launch: 2A0335+096 and PKS0745-191) are among the brightest cooling-flow clusters in H-alpha emission. We have already obtained very deep Palomar optical spectra of these clusters. Complementary ISO measurements of the Ne II (12.8 microns), Ne III (15.6 microns), Si II (35 microns), and O I (63 microns) lines will provide unique information about both the ionized gas and any neutral gas also present. The [Ne III]/[Ne II] ratio responds sensitively to the spectral shape of the ionizing radiation, helping to identify the currently unknown mechanism powering the nebulae. The [Si II] flux indicates the silicon depletion and thus the dust content and origin of the nebular gas. The [O I] flux reveals the total amount of neutral X-ray heated gas and will show whether a large mass of hitherto unseen condensed gas lies at the centers of cooling flows. Measurements of [O I] with the LWS will also yield deep, sparsely- sampled, far-IR continuum spectra of these clusters suitable for studying their dust contents.