ROSAT HRI images were obtained for two clusters of galaxies which contain strong cooling flows, A2029 and 2A0335+096. These observations confirm that gas is cooling at rates of M˙c≈370M⊙yr−1 in A2029 and M˙c≈262M⊙yr−1 in 2A0335+096. In both clusters, the X-ray emission from the inner cooling flow regions (r ≳ 100 kpc) is very inhomogeneous, with the X-ray surface brightness being dominated by a number of X-ray emitting filaments. Using the crude spectral resolution of the HRI, we show that these filaments are the result of excess emission, rather than foreground X-ray absorption. Although there are uncertainties in the pointing, many of the X-ray features in the cooling flow region of 2A0335+096 correspond to features in Hα optical line emission. This indicates that the 104 K gas originates through the cooling of hot X-ray emitting gas. The gas is the filaments is too dense to be in hydrostatic equilibrium, and it is likely that other forces such as rotation, turbulence, and magnetic fields influence the dynamical state of the gas. The filaments may be supported in part by magnetic fields and may be connected with the filaments of very strong Faraday rotation seen in several nearly cooling flows.