  We present a generalization of the concept of magnification bias for
gravitationally-lensed quasars, in which the quasars are selected by flux in
more than one wavelength band. To illustrate the principle, we consider the
case of two-band selection, in which the fluxes in the two bands are
uncorrelated, perfectly correlated, or correlated with scatter. For
uncorrelated fluxes, we show that the previously-held result - that the bias is
the product of the single-band biases - is generally false. We demonstrate some
important properties of the multi-band magnification bias using model
luminosity functions inspired by observed correlations among X-ray, optical,
infrared and radio fluxes of quasars. In particular, the bias need not be an
increasing function of each flux, and the bias can be extremely large for
non-linear correlations. The latter fact may account for the high lensing rates
found in some X-ray/optical and infrared/radio selected samples.
