The machine, either in a version for open vials or in one for closed vials, has a cantilevered architecture such that at the sides of the relative conveyor line of the vials there is a substantially vertical air passage gap developing in a downwards direction and connected with a conveyor which opens into an air outlet facing externally of the machine and positioned considerably below the conveyor line. The operating organs of the machine, among which the conveyor line, are inserted in a chamber having a controlled atmosphere, to which means for forced ventilation are associated, which means generate a laminar flow of air directed from above in a downwards direction. The part of the laminar flow, which strikes the sides of the conveyor line and the vials present therein, enters, without perturbation, the air passage gap and exits from the air outlet; thus entry of polluting particles into the inlet of the vials is prevented.