This paper studies the downstep phenomenon in Gwari, a West Benue-Congo language spoken in Nigeria and reports that high and mid tones are subject to downstepping in the language. The phenomenon is however blocked in syllables whose onsets contain voiceless obstruents. It is also reported that in the associative construction, the language marks the genitive relation with a floating high tonal morpheme (H-tomorph) that has the capability to dock directly onto the first tone bearing unit in the stem of the rightmost noun, whether that noun has a prefix or not. Downstep then arises when the docking of the tomorph is followed by the loss of a low toned prefix, and other structural conditions are met.