The Lotka--Volterra system of autonomous differential
equations consists in three homogeneous polynomial equations of degree 2
in three variables.
This system, or the corresponding vector field $\lv$, depends on three
non--zero (complex) parameters and may be written as
\[\lv= x (C y + z)\partial_x + y (A z + x)\partial_y + z ( B x +
y)\partial_z.\]In fact, $\lv$ can be chosen as a normal form for most of the factored
quadratic systems; the study of its first integrals of degree 0 is thus of
great mathematical interest.
In the paper into consideration \cite{jmo2001}, we thus described all
possible values of the triple $(A,B,C)$ of non--zero parameters for which
$\lv$ has a homogeneous liouvillian first integral of degree $0$.
We also discussed the corresponding problem of the liouvillian
integration for quadratic factored vector fields that cannot be put in
Lotka--Volterra normal form, for instance with some $0$ among $A,B,C$.
{\em There are some errors in the description of these marginal situations
that we would like to correct in the present note}.