The magnetic ions of the A -site spinels M Al2 O4 (M=Mn,Fe,Co) form a diamond lattice which, by means of competing interactions, are subject to strong frustration effects. In this paper we present the outcome of inelastic neutron-scattering experiments to investigate the corresponding magnetic excitations. MnAl2 O4 exhibits the strongest magnetic exchange and reveals long-range magnetic order below TN =40 K with a well-defined spin-wave dispersion. In contrast, CoAl2 O4 and FeAl2 O4 do not show long-range order but the magnetic scattering corresponds to a liquidlike structure factor. Inelastic neutron scattering in CoAl2 O4 shows a dispersionlike structure indicating collective magnetic excitations, despite the absence of long-range magnetic order. This type of behavior corresponds to a cooperative paramagnet. The opening of a spin gap in FeAl2 O4 is observed at low temperatures. These three A -site spinels are located on the border of long-range magnetic order with distinct emergent behavior. The corresponding role of orbital degrees of freedom is discussed.