Brittle films of ceramics on metal substrates become mechanically unstable when a critical thickness is exceeded. Experiments have been carried out to investigate this instability for films under tension and compression. Films of cerium oxide gel under tension were prepared by spin-coating a ceria sol onto stainless steel substrates. Films exceeding a critical thickness failed by through-film cracking. The relationship between crack spacing and film thickness was consistent with partial interfacial delamination accompanying film cracking. Films of nickel oxide under compression were prepared by the oxidation of nickel and NiAl and NiCr alloys. The adhesion of the films to the substrates was measured in a double bending beam configuration and by scratch testing. A critical thickness was observed at which adhesion became very low and which depended on the composition of the metal substrate. The observed behaviour is consistent with a buckling instability in the film. In both types of film the conditions for crack propagation appear to determine instability, but the nature of the failure-initiating defects remains obscure.