This paper investigates the sequential logics for modal Ockham algebras, which are Ockham algebras with normal modal operators \(\Box ,\Diamond \) satisfying interaction axioms. Relational semantics are established for this logic, and discrete duality is shown using star semantics. We then obtain the Kripke-completeness for this logic and some common modal extensions by the canonical model method. Furthermore, we extend existing results, which are based on modal Ockham algebra, to each modal Berman variety.