  The response of mesoscopic superconductors to an ac magnetic field is
numerically investigated on the basis of the time-dependent Ginzburg-Landau
equations (TDGL). We study the dependence with frequency $\omega$ and dc
magnetic field $H_{dc}$ of the linear ac susceptibility $\chi(H_{dc}, \omega)$
in square samples with dimensions of the order of the London penetration depth.
At $H_{dc}=0$ the behavior of $\chi$ as a function of $\omega$ agrees very well
with the two fluid model, and the imaginary part of the ac susceptibility,
$\chi"(\omega)$, shows a dissipative a maximum at the frequency
$\nu_o=c^2/(4\pi \sigma\lambda^2)$. In the presence of a magnetic field a
second dissipation maximum appears at a frequency $\omega_p\ll\nu_0$. The most
interesting behavior of mesoscopic superconductors can be observed in the
$\chi(H_{dc})$ curves obtained at a fixed frequency. At a fixed number of
vortices, $\chi"(H_{dc})$ continuously increases with increasing $H_{dc}$. We
observe that the dissipation reaches a maximum for magnetic fields right below
the vortex penetration fields. Then, after each vortex penetration event, there
is a sudden suppression of the ac losses, showing discontinuities in
$\chi"(H_{dc})$ at several values of $H_{dc}$. We show that these
discontinuities are typical of the mesoscopic scale and disappear in
macroscopic samples, which have a continuos behavior of $\chi(H_{dc})$. We
argue that these discontinuities in $\chi(H_{dc})$ are due to the effect of
{\it nascent vortices} which cause a large variation of the amplitude of the
order parameter near the surface before the entrance of vortices.
