  In this paper we determine the generalized Weierstrass semigroup $
\widehat{H}(P_{\infty}, P_1, \ldots , P_{m})$, and consequently the Weierstrass
semigroup $H(P_{\infty}, P_1, \ldots , P_{m})$, at $m+1$ points on the curves
$\mathcal{X}_{a,b,n,s}$ and $\mathcal{Y}_{n,s}$. These curves has been
introduced in Tafazolian et al. as new examples of curves which cannot be
covered by the Hermitian curve.
