We present measurements of the upper critical magnetic field Hc2(T) determined from the dc magnetization of polycrystalline samples of U(1-x)ThxBe13 with x=0 and x=0.0331 and a single crystal of pure UBe13. We find changes in slope in the Hc2 vs T phase diagrams of both polycrystalline samples which suggests entrance into a second superconducting phase at about Tc2. A degradation of the superconducting critical field is observed in the single crystal which may be related to the absence of second-phase behavior in this sample. Our results are discussed in light of recent experimental and theoretical treatments of second-phase behavior in heavy-fermion superconductors. © 1988 The American Physical Society.