  The off--shell electromagnetic vertex function of pions and kaons is studied
in a bosonized Nambu--Jona-Lasinio model with a gauge--invariant proper--time
cutoff. The slope of the pion form factor with respect to the pion 4--momentum
is found to be equal to the on--shell pion charge radius in the chiral limit.
The off--shell slope of the $K^0$ form factor is zero, that of the $K^\pm$
about 15\% smaller than that of the pion. We compare our results with those of
a recent calculation in chiral perturbation theory.
