Stratified adaptive cluster sampling refers to designs in which, following an initial stratified sample, additional units are added to the sample from the neighbourhood of any selected unit with an observed value that satisfies a condition of interest. If any of the added units in turn satisfies the condition, still more units are added to the sample. Estimation of the population mean or total with the stratified adaptive cluster designs is complicated by the possibility that a selection in one stratum may result in the addition of units from other strata to the sample, so that observations in separate strata are not independent. Since conventional estimators such as the stratified sample mean are biased with the adaptive designs of this paper, several types of estimators are developed which are unbiased for the population mean or total with stratified adaptive cluster sampling.