  Main interest of the present paper is to investigate the almost
{\alpha}-cosymplectic manifolds for which the characteristic vector field of
the almost {\alpha}-cosymplectic structure satisfies a specific
({\kappa},{\mu},{\nu})-nullity condition. This condition is invariant under
D-homothetic deformation of the almost cosymplectic
({\kappa},{\mu},{\nu})-spaces in all dimensions. Also, we prove that for
dimensions greater than three, {\kappa},{\mu},{\nu} are not necessary constant
smooth functions such that df^{\eta}=0. Then the existence of the
three-dimensional case of almost cosymplectic ({\kappa},{\mu},{\nu})-spaces are
studied. Finally, we construct an appropriate example of such manifolds.
