The identification of outliers in data has been an area of a great deal of attention for many years. The outlier detection procedure is more cumbersome in regression where outliers may occur in the response variable or in the explanatory variables or both. A variety of diagnostic methods are now being used for the identification of different types of outliers in regression. These methods, however, are successful only if the data set contains a single outlier. In the presence of multiple outliers diagnostic methods often fail to detect the outliers. This is due to the well-known problems of masking and swamping effects. On the other hand the robust methods can identify the outliers correctly but they are too prone to declare observations to be outlier which is not also desired. In this paper we discuss an approach which is a compromise between these two approaches. We call this approach diagnostic-robust approach where the suspect outliers are identified first by robust methods and diagnostic methods are applied later to confirm the suspicion. We consider several well-known data sets to investigate the performance of the diagnostic-robust approach in the detection of outliers in regression.