We present the results of an analysis of the WC10 central stars CPD - 56 degrees 8032 and He 2-113 and of their surrounding planetary nebulae (PNe). UCL Echelle Spectrograph spectra with a resolving power of R = 50 000, covering the wavelength range 3600-9500 Angstrom, were obtained for both objects. Expansion and radial velocities are derived from the nebular Balmer lines. Reddenings were derived from the observed H alpha/H beta decrements, as well as from the ratio of the radio free-free and H beta fluxes. We find that E(B - V) = 0.68 for CPD - 56 degrees 8032 and 1.00 for He 2-113. The bolometric luminosity is found to be 2820 D-2 (kpc) L. for CPD - 56 degrees 8032 and 2290 D-2 (kpc) L. for He 2-113. We have used a calibration based on Magellanic Cloud Wolf-Rayet central stars to estimate a distance of 1.35 kpc to CPD - 56 degrees 8032 and 1.50 kpc to He 2-113. A comparison of the radial velocities of interstellar Na I D-line absorption components with Galactic rotation curve predictions for each line of sight yields distances which agree within the uncertainties with these values. We also present deconvolved pre-COSTAR HST H beta images, from which we derive nebular angular sizes of 1.6 x 2.1 arcsec(2) for CPD - 56 degrees 8032 and 1.4 x 1.1 arcsec(2) for He 2-113. From our spectra, nebular electron temperatures of 8800 and 8400 K are derived for CPD - 56 degrees 8032 and He 2-113 respectively, while an electron density of 6 x 10(4) cm(-3) is determined for both nebulae. Sulphur is found to have a near-solar abundance in both nebulae, and the nebular nitrogen abundances are also close to solar. The nebular C/O abundance ratios (determined with the help of low-resolution IUE spectra) are found to be equal to 13 for CPD - 56 degrees 8032 and 10 for He 2-113, respectively, significantly higher than the values normally found for Galactic PNe. We iind no detectable amounts of hydrogen in either stellar wind.