  We give two constructions of grading-restricted vertex (super)algebras. We
first give a new construction of a class of grading-restricted vertex
(super)algebras originally obtained by Meurman and Primc using a different
method. This construction is based on a new definition of vertex operators and
a new method. Our second construction is a generalization of the author's
construction of the moonshine module vertex operator algebra and a related
vertex operator superalgebra. This construction needs properties of
intertwining operators formulated and proved by the author.
