Abstract: A structure is observed in the B±K∓ mass spectrum in a sample of proton–proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, collected with the LHCb detector and corresponding to a total integrated luminosity of 9fb-1. The structure is interpreted as the result of overlapping excited Bs0 states. With high significance, a two-peak hypothesis provides a better description of the data than a single resonance. Under this hypothesis the masses and widths of the two states, assuming they decay directly to B±K∓, are determined to be m1=6063.5±1.2(stat)±0.8(syst)Me, Γ1=26±4(stat)±4(syst)Me, m2=6114±3(stat)±5(syst)Me, Γ2=66±18(stat)±21(syst)Me.Alternative values assuming a decay through B∗±K∓, with a missing photon from the B∗±→B±γ decay, which are shifted by approximately 45MeV, are also determined. The possibility of a single state decaying in both channels is also considered. The ratio of the total production cross-section times branching fraction of the new states relative to the previously observed Bs2∗0 state is determined to be 0.87±0.15(stat)±0.19(syst).