Asymptotic expansions are given for large values of $n$ of the generalized
Bernoulli polynomials $B_n^\mu(z)$ and Euler polynomials $E_n^\mu(z)$. In a
previous paper L\'opez and Temme (1999) these polynomials have been considered
for large values of $\mu$, with $n$ fixed. In the literature no complete
description of the large $n$ asymptotics of the considered polynomials is
available. We give the general expansions, summarize known results of special
cases and give more details about these results. We use two-point Taylor
expansions for obtaining new type of expansions. The analysis is based on
contour integrals that follow from the generating functions of the polynomials.