  By using the Hamilton-Jacobi [$HJ$] framework the higher-order
Maxwell-Chern-Simons theory is analyzed. The complete set of $HJ$ Hamiltonians
and a generalized $HJ$ differential are reported, from which all symmetries of
the theory are identified. In addition, we complete our study by performing the
higher order Gitman-Lyakhovich-Tyutin [$GLT$] framework and compare the results
of both formalisms.
