Many models of asymmetric distributions proposed in the statistical literature are obtained by transforming an arbitrary symmetric distribution by means of a skewing mechanism. In certain important cases, the resultant skewed distribution shares some properties of its symmetric antecedent. Because of this inheritance, it would be interesting to test if the symmetric generator belongs to a certain family, that is to say, testing goodness-of-fit for the symmetric component. This work proposes a test of such hypothesis. Taking into account that the normal law is perhaps the most studied distribution, as a particular case of unquestionable interest, the generalized skew-normal family is studied in detail, because the symmetric component of the distributions in this family is normal.