We report detailed spatially resolved spectroscopy of the WR nebulae NGC 2359 and RCW 78 surrounding the WN 5 HD 56925 and WN 8 HD 117688 stars. The aim of this work has been to study possible abundance inhomogeneities and the ionization structure of the nebulae, as well as to derive reliable values for the degree of self-enrichment. In NGC 2359 the derived ratio O2+/O+ shows localized variations resulting from the compression of the gas in the filaments with respect to the shell gas. Effective temperatures for the central stars of both nebulae have been estimated on the basis of the ionization structure; the values found appear appropriate for their spectral types. Abundances of O/H, NIH, Ne/H, and He/H have been determined in twelve different positions in NGC 2359, covering its different morphological zones. No significant differences in the N/H and O/H abundances across the nebula have been found, although He/H shows marginal evidence for localized enhancements. In the case of RCW 78 the derived value of O/H is roughly solar, but He/H and NIH may be slightly overabundant. The results suggest that the amount of chemical self-enrichment of these WR nebulae is, at most, small.