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 presents 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 $\vartheta_{23}$ and $\vartheta_{24}$, and they contain as limiting cases the pure solar $\nu_e$-active and $\nu_e$-sterile neutrino oscillations, and the pure atmospheric $\nu_\mu\to\nu_s$ and $\nu_\mu\to\nu_\tau$ 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 disfavour both the pure $\nu_\mu\to\nu_s$ atmospheric channel and the pure $\nu_e\to\nu_s$ solar channel, the result from the combined analysis still favours close-to-pure active and sterile oscillations and disfavours oscillations into a near-maximal active-sterile admixture.