Spin excitations stemming from the metallic phase of the ferrochalcogenide superconductor K0.77Fe1.85Se2 (T-c = 32 K) were mapped out in the ab-plane by means of the time-of-flight neutron spectroscopy. We observed a magnetic resonant mode at Q(res) = (1/2 1/4), whose energy and in-plane shape are almost identical to those in the related compound Rb0.8Fe1.6Se2. This lets us infer that there is a unique underlying electronic structure of the bulk superconducting phase KxFe2Se2, which is universal for all alkali-metal iron selenide superconductors and stands in contrast to the doping-tunable phase diagrams of the related iron pnictides. Furthermore, the spectral weight of the resonance on the absolute scale, normalized to the volume fraction of the superconducting phase, is several times larger than in optimally doped BaFe2-xCoxAs2. We also found no evidence for any additional low-energy branches of spin excitations away from Qres. Our results provide new input for theoretical models of the spin dynamics in iron-based superconductors. open access Copyright (C) EPLA, 2012