Specific heat C(T) and upper critical field Hc2(T) measurements have been performed on two single crystal specimens (denoted A and B) of the antiferromagnetic heavy-electron superconductor URu2Si2. Specific heat measurements on both single crystals reveal two distinct jumps, indicative of two superconducting phases. This is reminiscent of the antiferromagnetic heavy-electron compound UPt3 in which multiple superconducting transitions have been observed and attributed to coupled antiferromagnetic and multicomponent superconducting order parameters, although two superconducting phases associated with two different states of the crystal cannot be ruled out. The relative magnitudes of the two specific heat jumps observed in crystal B suggest that the two superconducting phases occupy nearly equal volume fractions of the crystal. At temperatures below the lower jump, the specific heat of both crystals can be described by C3(T) = γs(0)T+AT3 with γ3(0) ≈ 0.5γn(0), where γn(0) is the value of the normal-state electronic specific heat coefficient γn(T), extrapolated to T = 0. The two critical temperatures inferred from the specific heat jumps in crystal B, measured in magnetic fields H between 0 and 15kOe applied parallel to the c-axis, have a similar dependence on H. Resistive measurements of Hc2(T) on specimens from crystal A between 0 and 60 kOe reveal a kink near 2 kOe for H⌈c and strong positive curvature in Hc2(T) below ∼3 kOe for H⌈a. © 1991.