We present an analysis of the neutrino oscillation solutions of the solar and atmospheric neutrino problems in the framework of four-neutrino mixing where a sterile neutrino is added to the three standard ones and the mass spectra present two separated doublets. Such scenarios allow for simultaneous transitions of solar nu (e), as well as atmospheric nu (mu), into active and sterile neutrinos controlled by the additional mixing angles theta (23) and theta (24), and they contain as limiting cases the pure solar nu (e)-active and nu (e)-sterile neutrino oscillations, and the pure atmospheric nu (mu)--> nu (s) and nu (mu)--> nu (tau) oscillations, respectively. We evaluate the allowed active-sterile admixture in both solar and atmospheric oscillations from the combined analysis, Our results show that, although the Super-Kamiokande data disfavor both the pure nu (mu)--> nu (s) atmospheric channel and the pure nu (e)--> nu (s) solar channel, the result from the combined analysis still favors close-to-pure active and sterile oscillations and disfavors oscillations into a near-maximal active-sterile admixture.