  In this paper we elaborate on the structure of the Generalized Lotka-Volterra
(GLV) form for nonlinear differential equations. We discuss here the algebraic
properties of the GLV family, such as the invariance under quasimonomial
transformations and the underlying structure of classes of equivalence. Each
class possesses a unique representative under the classical quadratic
Lotka-Volterra form. We show how other standard modelling forms of biological
interest, such as S-systems or mass-action systems are naturally embedded into
the GLV form, which thus provides a formal framework for their comparison, and
for the establishment of transformation rules. We also focus on the issue of
recasting of general nonlinear systems into the GLV format. We present a
procedure for doing so, and point at possible sources of ambiguity which could
make the resulting Lotka-Volterra system dependent on the path followed. We
then provide some general theorems that define the operational and algorithmic
framework in which this is not the case.
