Scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDX) has indicated that adherent crack-free coatings of amorphous SiC and "Si3N4/Si2N2O" can be built up on planar alumina substrates by pyrolysis of layers of polycarbosilane (PCS) and poly(diphenyl)silazane (PDPS) precursors applied by spin- or dip-coating methods. In general, multilayers of black SiC can be prepared by pyrolysis of PCS layers at 1100-degrees-C in a nitrogen atmosphere while transparent coatings consisting of multiple layers of Si3N4 are prepared by pyrolysis of either PCS or PDPS layers in a flowing atmosphere of ammonia at 1100-degrees-C. The "Si3N4/Si2N2O" layers prepared by pyrolysing spin-coated layers of PDPS layers are found to be superior in quality (with respect to blemishes and embedded debris) than those prepared from spin-coated layers of PCS. Microhardness tests reveal that the coatings derived from PCS and PDPS are significantly softer than would be expected for SiC and Si3N4. X-ray photoelectron studies reveal that the surface of the PCS-derived SiC coatings consists of an SiO2 layer while the surface of the PDPS-derived "Si3N4/Si2N2O" coating consists of an oxygen-rich silicon oxycarbonitride. These results are also generally supported by Rutherford backscattering spectra which also indicate considerable phase mixing of silicon, carbon, oxygen and nitrogen components within the bulk of the SiC and "Si3N4/Si2N2O" coatings on alumina.