  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.
