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At the basis of many capture-recapture sampling models is the assumption that all animals are equally likely to be caught in each sample (The Equal Catchability Assumption). This assumption is often violated in wildlife populations (Seber 1973:81) and 2 general types of alternatives exist (Pollock 1981): (1) Heterogeneity: The probability of capture in any sample is a property of the animal and may vary over the population. That is, animals may vary in capture probabilities according to age, sex, social status, and many other factors. (2) Trap response: The probability of capture in any sample depends on the animal's prior history of capture. That is, animals may become shy or happy depending upon the type of trapping method used. Either 1 or both of these 2 types of alternatives may be acting in a particular animal population. The traditional capture-recapture model used by biologists for closed populations (populations closed to additions or deletions) in short-term studies is the Schnabel Model (Schnabel 1938) that requires The Equal Catchability Assumption. In recent years there has been substantial research on models for closed populations that allow heterogeneity and/or trap response of the capture probabilities. Otis et al. (1978) published an important monograph on these models that allows their routine use by biologists. The capture-recapture model becoming used by biologists for open populations in long-term studies is the Jolly-Seber Model (Seber 1973). This model requires The Equal Catchability Assumption and the complexity of open population models is likely to preclude general models that allow heterogeneity and/or trap response. During the preparation of a review of capture-recapture methods (Pollock 1981), I realized that statisticians have drawn a sharp distinction between closed and open population models that is perhaps rather artificial. Here I describe a design for long-term studies that is robust to heterogeneity and/or trap response. It allows an analysis that uses methodology from closed and open population models. There is a brief examination of its robustness properties using simulation and an example is given in detail to illustrate the methodology for biologists.