1. Two-level data, in which level-1 units or individuals are nested within level-2 units or clusters, are very com- mon in natural populations.However, very few multilevel analyses are conducted for data with imperfect detec- tion of individuals. Multilevel analyses are important to quantify the variability at each level of the data. 2. In this study, we present two-level analyses for estimating demographic parameters from data with imperfect detection of individuals and with a source of individual variability that is nested within a source of cluster vari- ability. 3. This method allows separating and quantifying the phenotypic plasticity or facultative behavioural responses from the evolutionary responses.We illustrate our approach using data from studies of a long-lived perennially monogamous seabird, the Cory's shearwater (Calonectris diomedea) and a patchy population of collared fly- catchers (Ficedula albicollis). 4. Wedemonstrate the existence of dependence in recapture probability between paired individuals in the Cory's shearwater. In addition, we show that family structure has no influence on parent–offspring resemblance in col- lared flycatchers dispersal. 5. The new method is implemented in programE-SURGE which is freely available from the internet.