  We consider the problem of determining Weierstrass gaps and pure Weierstrass
gaps at several points. Using the notion of relative maximality in generalized
Weierstrass semigroups due to Delgado \cite{D}, we present a description of
these elements which generalizes the approach of Homma and Kim \cite{HK} given
for pairs. Through this description, we study the gaps and pure gaps at several
points on a certain family of curves with separated variables.
