The ternary rare earth compound SmRh4B4 has been studied by means of upper critical field, low temperature specific heat, and static magnetic susceptibility measurements. A lambda-type specific heat anomaly, a discontinuity in the slope of the upper critical field versus temperature curve, and a cusp-like feature in the magnetic susceptibility suggest that superconductivity and long-range antiferromagnetic order coexist in SmRh4B4 below 0.87 K. Machida's theory for antiferromagnetic superconductors provides a good description of the upper critical field data, while the magnetic susceptibility data can be represented as the sum of a Curie-Weiss term with microeff = 0.632 microB and θp = -1.93 K and a temperature independent Van Vleck contribution. © 1979.