An apparatus comprises a moving arrangement for supporting and moving along an advance direction a plurality of articles; and orienting units movable along said advance direction and such as to contact and orient the articles by displacing angularly each article around an axis thereof so as to position the articles in respective output positions, the orienting units being such as to maintain the articles in contact with the moving arrangement, a detector being provided for each orienting unit for detecting an initial angular position of a respective article associated thereto and for promoting a desired angular displacement such that each article is brought in the output position.