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We present the results of a search for neutral Higgs bosons produced in association with b quarks in pp̅→ bb̅bb̅ final states with 91 ± 7 pb-1 of pp̅ collisions at √s =1.8 TeV recorded by the Collider Detector at Fermilab. We find no evidence of such a signal and the data are interpreted in the context of the neutral Higgs sector of the minimal supersymmetric extension of the standard model. With basic parameter choices for the supersymmetric scale and the stop-quark mixing, we derive 95% C.L. lower mass limits for neutral Higgs bosons for tanb values in excess of 35.