In this paper, we detect hallucinations in summaries generated by abstractive summarization models. We focus on three types of hallucination viz. intrinsic, extrinsic, and nonhallucinated. The method used for detecting hallucination is based on textual entailment. Given a premise and a hypothesis, textual entailment classifies the hypothesis as contradiction, neutral, or entailment. These three classes of textual entailment are mapped to intrinsic, extrinsic, and non-hallucinated respectively. We fine-tune a RoBERTa-large model on NLI datasets and use it to detect hallucinations on the XSumFaith dataset. We demonstrate that our simple approach using textual entailment outperforms the existing factuality inconsistency detection systems by 12% and we provide insightful analysis of all types of hallucination. To advance research in this area, we create and release a dataset, XSumFaith++, which contains balanced instances of hallucinated and non-hallucinated summaries.