The first-order valence transition in has been investigated for single crystalline samples with x = 0.32 and x = 0.35 as well as for polycrystalline samples with (x varied in steps of 0.01) through the measurements of magnetic susceptibility, . For the single crystal with x = 0.32, exhibits a strong anisotropic mixed-valence behaviour. On the other hand, of the crystal with x = 0.35 exhibits a sharp first-order valence transition at 50 K. In both crystals, the strong anisotropy, , is maintained as in the host compound CeNiSn. The arc-melted polycrystalline alloys with a narrow range of Co composition, x = 0.33-0.37, show a sharp drop in below 70 K and large hysteresis. This transition becomes sharper by annealing at . For the optimum concentration x = 0.35, the drop in at the transition becomes as high as 72% for the single crystal and 69% for the polycrystalline alloy for which a jump in ac heat capacity was observed at 55 K. Analysis of the above results reveals that the phase transition involves a large change in the Kondo temperature . The small volume discontinuity at the transition suggests that the phase transition is not due to a Kondo volume collapse. A possible mechanism responsible for the phase transition in the present alloys is proposed.