A Weibull analysis is presented of the dose and time relationships for the effects on 4080 inbred rats of chronic ingestion in the drinking water of 16 different doses of N-nitrosodimethylamine (NDMA) or N-nitrosodiethylamine (NDEA). The sites chiefly affected were the liver (by both agents) and the esophagus (by NDEA only). Since the experiment continued on into extreme old age, effects became measurable at doses of only 0.01 to 0.02 mg/kg/day, which is an order of magnitude lower than previously achieved. (After only 2 years of treatment, however, the TD50 doses needed to halve the proportion of tumorless survivors would have been about 0.06 mg/kg/day of NDEA, or about 0.12 mg/kg/day of NDMA.) The general pattern of response was that the natural logarithm of the probability of remaining tumorless was given by the product of two terms, the first (the "Weibull b value") depending on the dose rate but not on the duration of exposure and the second depending not on dose at all but only on duration. For all types of tumor the dependence on duration was fairly similar (and for each the second term was taken to be -t7, where t = years of treatment), but for different types of tumor the dependence on dose rate was quite different. For esophageal tumors, the "Weibull b value" was approximately proportional to the cube of the dose rate of NDEA (males 21 d3, females 11 d3, where d = dose rate in mg/kg adult body weight/day), and the background incidence was unmeasurably low. For liver tumors induced by NDEA, the b value was approximately proportional to the fourth power of dose rate + 0.04 mg/kg/day [males, 19 (d + 0.04)4; females, 32 (d + 0.04)4], although the relationships were somewhat different for the different cell types of liver tumor. This one formula implies both approximate linearity at low doses and an approximately cubic relationship within the higher range of doses that was studied. For liver tumors induced by NDMA, the Weibull b value was approximately proportional to the sixth power of dose rate + 0.1 mg/kg/day [males, 37 (d + 0.1)6; females, 51 (d + 0.1)6], again with some variation between liver cell types, and again implying approximate linearity at low doses. These algebraic formulae should, of course, be trusted only in the range of doses where they were derived, and particularly not above it.(ABSTRACT TRUNCATED AT 400 WORDS)