Globally framed

-manifolds are studied from the point of view of the curvature. Generalized globally framed

-space-forms are introduced and the interrelation with generalized Sasakian and generalized complex space-forms is pointed out. Suitable differential equations allow to discuss the constancy of the

-sectional curvatures. Further results are stated when the underlying structure is a

-structure or an

-structure of Kenmotsu type.