  Consider a stochastic process $\mathfrak{X}$, regenerative at a state $x$
which is instantaneous and regular. Let $L$ be a regenerative local time for
$\mathfrak{X}$ at $x$. Suppose furthermore that $\mathfrak{X}$ can be
approximated by discrete time regenerative processes $\mathfrak{X}^n$ for which
$x$ is accesible. We give conditions on $\mathfrak{X}$ and $\mathfrak{X}^n$ so
that the naturally defined local time of $\mathfrak{X}^n$ converges weakly to
$L$. This limit theorem generalizes previous invariance principles that have
appeared in the literature.
