  The resistivity minima of the quantum Hall effect arise due to the
localization of the electron states at the Fermi energy, when it is positioned
between adjacent Landau levels. In this paper we calculate the localization
length $\xi$ of such states at even filling factors $\nu = 2 N$. The
calculation is done for several models of disorder (``white-noise,''
short-range, and long-range random potentials). We find that the localization
length has a power-law dependence on the Landau level index, $\xi \propto
N^\alpha$ with the exponent $\alpha$ between one and ${10/3}$, depending on the
model. In particular, for a ``white-noise'' random potential $\xi$ roughly
coincides with the classical cyclotron radius. Our results are in reasonable
agreement with experimental data on low and moderate mobility samples.
