Abductive reasoning involves generating an explanation for a given set of observations about the world. Abduction provides a good reasoning framework for many AI problems, including diagnosis, plan recognition and learning. This paper focuses on the use of abductive reasoning in diagnostic systems in which there may be more than one underlying cause for the observed symptoms. In exploring this topic, we will review and compare several different approaches, including Binary Choice Bayesian, Sequential Bayesian, Causal Model Based Abduction, Parsimonious Set Covering, and the use of First Order Logic. Throughout the paper we will use as an example a simple diagnostic problem involving automotive troubleshooting.