[en] This paper considers entomological and epidemiological criteria for establishing the absence of tsetse and trypanosomosis associated with tsetse eradication programmes. The sampling goal is simple - to maximise the probability of detecting tsetse flies in the field or trypanosomes in hosts, if they exist. Sampling strategies cannot guarantee the absence of tsetse and trypanosomes but they can be used to estimate the probability of their eradication. Because tsetse eradication programmes are targeted at defined areas, geographical information system (GIS) tools are very useful in guiding spatial sampling strategies. Two approaches to assess tsetse eradication are discussed. The first depends only on information on the sensitivity of tsetse trapping methods used. The second combines information on pre-eradication tsetse trapping and the proportion of time during which no tsetse have been trapped, assuming either a stable or declining (preferred) pre-eradication tsetse population. For establishing the absence of trypanosomosis in host populations, there are standard sampling techniques that can be adjusted for the sensitivity and specificity of the trypanosome detection methods used. Required sample sizes can be calculated for both direct trypanosome detection methods of 100% specificity or indirect tests with imperfect sensitivity and specificity. For the latter, both the sample size and the number of reactors (assumed to be false positive) are estimated for the required confidence level. These entomological and epidemiological methods were then applied to assess the eradication of tsetse and trypanosomosis from Unguja island of Zanzibar using the sterile insect technique (SIT). Pre- and post-eradication data collected were sufficient to establish with 95% confidence that both tsetse and trypanosomosis were eradicated. (author)