On stability of $N$-times integrated semigroups with nonquasianalytic growth

We discuss the behaviour at infinity of $n$-times integrated semigroups with nonquasianalytic growth and invertible generator. The results obtained extend in this setting a theorem of O. El Mennaoui on stability of bounded once integrated semigroups, and (partially) a theorem of Q. P. V$\tilde{\mathrm{u}}$ on stability of $C_0$-semigroups.