The purpose of this paper is to study a new class of framed manifolds. Such manifolds are Called almost alpha-cosymplectic f-manifolds. For some special cases of alpha and s, one obtains (almost) alpha-cosymplectic, (almost) C-manifolds, and (almost) Kenmotsu f-manifolds. Moreover, several tensor conditions are studied. We conclude our results with a general example on alpha-cosymplectic f-manifolds.