High-resolution spectroscopic observations have been obtained for the Wolf-Rayet galaxies He 2-10, II Zw 40, POX 4, and Tol 35. Several subregions have been selected in each slit position in order to investigate possible spatial variations in the line profiles, radial velocities, and ionization conditions of the gas. The most remarkable feature of the spectra is the presence of asymmetric broad low-intensity wings in the profiles of the brightest emission lines. These spectral features are detected farther out from the star-forming knots, showing linear dimensions between 300 pc and 4.1 kpc. The maximum expansion velocity measured for this gas is between 120 and 340 km s-1 and appears to be quite constant along the slit for all the objects. Additional general properties of the spectra are (1) the quoted emission-line ratios are similar in the narrow and broad components, (2) no systematic differences of the behavior of the broad and narrow components have been found along the major and minor axis of the galaxies, and (3) the spatial distribution of the ionized gas is peaked centrally. Different mechanisms capable of producing the observed broad spectral features are discussed: cloud-cloud collisions in virialized gas, "academic" superbubbles, champagne flows, and superbubble blowout. It is concluded that superbubble blowout expanding over a cloudy medium can explain the observational properties in a reasonable manner.