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We report results of a study of the Bs0 oscillation frequency using a large sample of Bs0 semileptonic decays corresponding to approximately 1 fb-1 of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron Collider in 2002–2006. The amplitude method gives a lower limit on the Bs0 oscillation frequency at 14.8 ps-1 at the 95% C.L. At Δms = 19 ps-1, the amplitude deviates from the hypothesis A= 0 (1) by 2.5 (1.6) standard deviations, corresponding to a two-sided C.L. of 1% (10%). A likelihood scan over the oscillation frequency, Δms, gives a most probable value of 19 ps-1 and a range of 17 < Δms < 21 ps-1 at the 90% C.L., assuming Gaussian uncertainties. This is the first direct two-sided bound measured by a single experiment. If Δms lies above 22 ps-1, then the probability that it would produce a likelihood minimum similar to the one observed in the interval 16–22 ps-1 is (5.0 ± 0.3)%.