Closed-population capture–recapture methods have been used extensively in animal ecology, both by themselves and within the context of Pollock’s robust design and multistate models, to estimate various parameters of population and community dynamics. The defining assumption of geographic and demographic closure (i.e., no births, deaths, immigration, or emigration) for the duration of sampling is restrictive and is likely to be violated in many field situations. I evaluated several types of violations of the closure assumption and found that completely random movement in and out of a study area does not introduce bias to estimators from closed-population methods, although it decreases precision. In addition, if capture probabilities vary only with time, the closed-population Lincoln-Petersen estimator is unbiased for the size of the superpopulation when there are only births/immigration or only deaths/emigration. However, for other cases of nonrandom movement, closed-population estimators were biased when movement was Markovian (dependent on the presence/absence of the animal in the previous time period), when an animal was allowed one entry to and one exit from the study area, or when there was trap response or heterogeneity among animals in capture probability. In addition, the probability that an animal is present and available for capture (e.g., breeding propensity) can be estimated using Pollock’s robust design only when movement occurs at a broader temporal scale than that of sampling.