The condition of normality is required for Standard statistical procedures. the results of these methods will be in. improper when the normality in not satisfied. There for, the normality assumption is required before proceeding most statistical analysis. There are many tests available to assess the assumption of normality, these tests do not have the same nature and power to diagnose the departures of data from normality, there for the choice of appropriate test always remain an important key in the assessment of normality    In this article and due to the importance of this subject and wide spread development of normality tests, a comprehensive Power comparison study of existing and new developed tests for normality is proposed. This study addresses the performance of 36 normality tests, for various sample sizes, considering several significance levels and for a number of symmetric and asymmetric distributions. General results for normality testing from this study are discussed according to the nature of alternative distribution.