We present the results on magnetovolume anomalies in (Fe1−xNix)49Rh51 alloys. At ambient pressure, they exhibit phase transition from the ferro- to the antiferromagnetic state at temperatures decreasing from about 300 to 150 K for x increasing from 0 to 0.036. The thermal expansion and compressibility of the alloys with x=0.025 and 0.045 were measured under high hydrostatic pressure up to 14 kbar. The phase transition to the antiferromagnetic state was induced in the alloy with x=0.045 by critical pressure of about 2.4 kbar. In the result of the phase transition to the antiferromagnetic state the volume decrease in the both alloys reaches the value of about 0.8%. The critical temperature Tt increases under pressure with the ratio of 9 and 13 K/kbar for x=0.025 and 0.045, respectively.