A triplet \((\omega , \mathcal {F}_{1},\mathcal {F}_{2})\)  is a bilagrangian structure on a manifold M, if \(\omega \) is a 2-form, closed and non-degenerate (called symplectic form) on M, and \((\mathcal {F}_{1},\mathcal {F}_{2})\) is a pair of transversal Lagrangian foliations on the symplectic manifold \((M,\omega )\) . The quadruplet \((M, \omega , \mathcal {F}_{1},\mathcal {F}_{2})\) is called a bilagrangian manifold. We prolong a bi-Lagrangian structure on M on its cotangent bundle \(T^{*}M\) in different ways. As a consequence, some dynamics on the set of bi-Lagrangian structures of M can be prolonged as dynamics on the set of the bi-Lagrangian structures of TM and \(T^{*}M\) .