In the superconductor Lu2Fe3Si5 (Tc=6.25 K) lutetium can be replaced by uranium up to a maximum of 40% [(Lu0.6U0.4)2Fe3Si5], maintaining the original P4/mnc structure. When the uranium content in (Lu1-xUx)2Fe2Si5 is increased the superconductivity vanishes and a heavy-fermion state is built up. Already for small amounts of uranium there is a strong suppression of superconductivity (Tc=1.8 K for x=0.01). According to the Abrikosov-Gorkov theory this suppression can be described by a strong exchange coupling between the uranium 5f electrons and the conduction electrons. In agreement with this high exchange coupling we detect drastically reduced magnetic (uranium) moments. For low dopings (x<0.1) there is no significant change of the Sommerfeld parameter γ. When the U content exceeds x>0.1 there is a strong γ increase. The enhanced specific heat remains unchanged when the sample is exposed to a magnetic field of 13 T. This field-independent specific heat, the screened magnetic moments, and the Wilson ratio χ/γ corroborate that the increase in γ is indeed indicative of an enhanced effective mass and not a result of magnetic entropy. Just like in other U-based systems (e.g., UPt3 and UBe13) the evolution of the heavy-fermion state in (UxLu1-x)2Fe3Si5 cannot merely be explained by a pure single-ion Kondo effect. The fact that the γ enhancement begins only after the U content exceeds x>0.1 points out that collective phenomena (i.e., interaction between the U ions) play a decisive role for the evolution of the heavy-fermion state in this system. Cerium-doped samples (Lu1-xCex)2Fe3Si5 revealed a distinctly weaker Tc suppression (Tc=1.9 K for x=0.1), less reduced magnetic moments, and no significant γ enhancement. © 1994 The American Physical Society.