1. The growth characteristics of a human hepatocellular carcinoma, derived from the PLC/PRF/5 cell-line (‘Alexander’), transplanted into sub-lethally irradiated athymic ( nu/nu ) mice have been examined. The xenograft re-expresses α-foetoprotein production although this tumour marker was not detected during cell culture in vitro. 2. There is a positive correlation between serum α-foetoprotein concentration and tumour mass ( r = 0.978), validating the use of this tumour marker to assess growth. 3. in mice with progressively growing xenografts there is a linear correlation between log serum α-foetoprotein concentration and time, compatible with exponential tumour growth. Growth of the human hepatocellular carcinoma xenograft is rapid, with an α-foetoprotein doubling time of 6.1 ± 2.1 days (±standard deviation) and a mass doubling time of 3.6 ± 1.2 days (±standard deviation). 4. The tumour cell birth or production rate, determined by a stathmokinetic (metaphase arrest) technique using vincristine, is 15.7 ± 3.8 (95% confidence limits) cells per 1000 cells per hour. The tumour cell loss factor (49%) is low and may contribute to the rapid growth of this human hepatocellular carcinoma xenograft.