Abstract
We present evidence that at the superconducting transition temperature Tc of the Heavy-Fermion-Superconductors CeCu2Si2 and Ube13, the order parameter is formed only on part of the Fermi-surface. In UBe13, at least part of the Fermi-surface that does not participate in superconductivity at Tc = 0.9K develops an order parameter in the accessible temperature range, i.e. at 0.55K. The effect can be sharply enhanced by doping UBe13 with a few at% Th, leading to a second phase transition within the superconducting state. In CeCu2Si2, those parts of the Fermi surface which do not participate in superconductivity down to the lowest temperatures carry a small effective mass. The influence of impurities on the Fermi-surface anisotropy is discussed.