We present an analysis of the neutrino oscillation solutions of the solar neutrino problem in the framework of four-neutrino mixing where a sterile neutrino is added to the three standard ones. We perform a fit to the full data set corresponding to the 825-day Super-Kamiokande data sample as well as to Chlorine, GALLEX and SAGE and Kamiokande experiments. In our analysis we use all measured total event rates as well as all Super-Kamiokande data on the zenith angle dependence and the recoil electron energy spectrum. We consider both transitions via the Mikheyev-Smirnov-Wolfenstein (MSW) mechanism as well as oscillations in vacuum (just-so) and find the allowed solutions for different values of the additional mixing angles. This framework permits transitions into active or sterile neutrinos controlled by the additional parameter $\cos^2(\vartheta_{23}) \cos^2(\vartheta_{24})$ . We discuss the maximum allowed values of this additional mixing parameter for the different solutions.

28 pages Latex file using RevTeX. 8 postscript figures included (bitmapped for compression). Detailed explanation of criterion 3 and lower two graphs of Fig. 8. Misprints corrected in table II.A full version of the paper can be found at http://ific.uv.es/~penya/papers/four/