In human conversations, ellipsis and coreference are commonly occurring linguistic phenomena. Although these phenomena are a mean of making human-machine conversations more fluent and natural, only few dialogue corpora contain explicit indications on which turns contain ellipses and/or coreferences. In this paper we address the task of automatically detecting ellipsis and coreferences in conversational question answering. We propose to use a multi-label classifier based on DistilBERT. Multi-label classification and active learning are employed to compensate the limited amount of labeled data. We show that these methods greatly enhance the performance of the classifier for detecting these phenomena on a manually labeled dataset.