In this paper, we study warped product anti-slant submanifolds of cosymplectic manifolds. It is shown that the cosymplectic manifold do not admit non trivial warped product submanifolds in the form N⊥ ×fNθ and then we obtain some results for the existence of warped products of the type Nθ ×fN⊥, where N⊥ and Nθ are anti-invariant and proper slant submanifolds of a cosymplectic manifold M¯ , respectively.