  By using the Hamilton-Jacobi [HJ] framework the higher-order
Maxwell-Chern-Simons theory is analyzed. We report the complete set of $HJ$
Hamiltonians and a generalized $HJ$ differential, 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.
