  The relationship between an algebra and its associated monomial algebra is
investigated when at least one of the algebras is $d$-Koszul. It is shown that
an algebra which has a reduced \grb basis that is composed of homogeneous
elements of degree $d$ is $d$-Koszul if and only if its associated monomial
algebra is $d$-Koszul. The class of 2-$d$-determined algebras and the class
2-$d$-Koszul algebras are introduced. In particular, it shown that
2-$d$-determined monomial algebras are 2-$d$-Koszul algebras and the structure
of the ideal of relations of such an algebra is completely determined.
