The　monitoring　of　a　categorical　process　with　serial　dependence　in　which　the　current　observation　depends　on　its　past　values　is　of　great　importance　in　many　applications,　including　manufacturing　and　service　management.　However,　a　great　majority　of　existing　research　works　are　restricted　to　the　cases　where　data　are　binary　and　of　first-order　dependency,　based　on　the　assumption　of　a　two-state　first-order　Markov　chain.　In　this　article,　a　general　categorical　process　with　serial　dependence　that　can　have　more　than　two　attribute　levels　and　higher-order　dependency　structure　is　under　consideration.　We　adopt　the　multivariate　representation　of　the　categorical　variables　and　integrate　directional　shift　information　into　an　adjusted　log-linear　model.　Based　on　this,　a　novel　control　chart　is　proposed　for　detecting　shifts　in　the　marginal　distribution　and　in　the　dependence　structure　of　serially　dependent　categorical　processes.　Simulations　have　demonstrated　its　efficiency　and　robustness.　The　implementation　of　the　proposed　control　chart　through　a　real　example　is　provided　as　the　guidance　for　practitioners.