If almost product $P$ or almost complex structure $J$ on the. tangent space $T(E)=T_V(E)+T_H(E)$ of Lagrangian $2n$ dimensional manifold $E$ are defined, and if $f_v(2k+1,1)$-structure on $T_V(E)$ is defined, then $f_p(2k+1,1)$ and $f_j(2k+1,1)$-structures on $T_H(E)$ are defined in the natural way. We can define $F_p(2k+1,1)$, $F_j(2k+1,1)$-struciurcs on $T(E)$. The condition is given for the reduction of the structural group of such manifolds.