  We introduce the notion of a non--linear Lie conformal superalgebra and prove
a PBW theorem for its universal enveloping vertex algebra. We also show that
conversely any graded freely generated vertex algebra is the universal
enveloping algebra of a non--linear Lie conformal superalgebra. This
correspondence will be applied in the subsequent work to the problem of
classification of finitely generated simple graded vertex algebras.
