We prove some structure results on Weierstrass points on a non-hyperelliptc curve, which are total or almost total ramification points for the gonal covering. It turns out that the corresponding Weierstrass semigroup is strictly related to the splitting type of the gonal scroll containing the canonical model of the curve. We also give a description of the Weierstrass gap sequence in the case of a non ramification point for the gonal cover
