The theory of $Osc^kM$ was introduced by R. Miron and Gh. Atanasiu in [3, 4]. R. Miron in [5, 6] gave the comprehensive theory of higher order geometry and its application. In  the subspaces of Miron's $Osc^kM$ was introduced and in  special adapted basis was constructed. Using the above results we examine different structures in the subspaces of $Osc^kM$.