Trace functions in the ring of fractions of polycyclic group rings, II We prove the existence of trace functions in the rings of fractions of polycyclic-by-finite group rings or their homomorphic images. In particular a trace function exists in the ring of fractions of $KH$, where $H$ is a polycyclic-by-finite group and $\char K > N$, where $N$ is a constant depending on $H$. Categories:20C07, 16A08, 16A39