  Classes of kinetic differential equations are delineated which do have a
quadratic first integral, and classes which can not have one. Example reactions
corresponding to the obtained kinetic differential equations are shown, and a
few figures showing the trajectories of the corresponding systems are also
included. Connections to other areas are mentioned and unsolved problems
collected. The new results are theoretical, although computational tools are
heavily used. Applications from biology and combustion theory will come later.
