  We generalize the sum rules for the nucleon electric plus magnetic
polarizability $\Sigma=\alpha+\beta$ and for the nucleon spin-polarizability
$\gamma$, to virtual photons with $Q^2>0$. The dominant low energy cross
sections are represented in our calculation by one-pion-loop graphs of
relativistic baryon chiral perturbation theory and the $\Delta(1232)$-resonance
excitation. For the proton we find good agreement of the calculated
$\Sigma_p(Q^2)$ with empirical values obtained from integrating up
electroproduction data for $Q^2<0.4 GeV^2$. The proton spin-polarizability
$\gamma_p(Q^2)$ switches sign around $Q^2= 0.4 GeV^2$ and it joins smoothly the
"partonic" curve, extracted from polarized deep-inelastic scattering, around
$Q^2=0.7 GeV^2$. For the neutron our predictions of $\Sigma_n(Q^2)$ and
$\gamma_n(Q^2)$ agree reasonably well at $Q^2=0$ with existing determinations.
Upcoming (polarized) electroproduction experiments will be able to test the
generalized polarizability sum rules investigated here.
