  Giant enhancement of the nonlinear response of a single crystal of Nb placed
in a sweeping magnetic field has been experimentally observed. The rectified
signal from Nb ($Tc=9.15$ K) has been measured by means of an inductive method
as a function of temperature, dc field, dc field sweep rate, and the amplitude
of ac field. The Nb sample was excited by an amplitude modulated ac field.
Under a stationary regime, the rectified signal appears only for magnetic
fields ($H_0$) in the range $H_{c2}<H_0<H_{c3}$ . However, when the dc field
was swept slowly, the rectified signal appears at $H_0>H_{c1}$. This experiment
shows that the amplitude of the rectified signal is two orders of magnitude
larger than the amplitude of the signal seen under stationary field conditions.
Moreover, the amplitude of the rectified signal is a power function of the
sweep rate, with the power exponent close to 1.
