We study the range of applicability of the weak-field approximation for the inference of magnetic field vectors from the profiles of the Stokes parameters. We show that, for typical solar lines in the visible, this approximation may be applied to an accuracy of approximately 20% for field strengths as great as 3500/g(L) G-where g(L) is the Lande factor-provided we work in the line wings. A systematic underestimate of the field strength seems to occur for strong fields-observations in several related spectral lines may allow a calibration of this effect, and so for an increase in accuracy of the inferences. The procedures have been tested using solar data obtained in two lines of Fe I, near 6300 angstrom, with the Stokes Polarimeter at the Mees Solar Observatory of the University of Hawaii.