The aim of the paper is to reconstruct the concept of natural necessity upon which the empirical causal (Humean) type of a scientific law rests and to enlarge the notion of the conditions of a scientific law. According to regularity theory, what counts in the investigation of causation is the universality of causal proposition. So in this theory priority is given to the explication of the concept “scientific law”. Such an explication was provided by Popper in the first edition of his Logik der Forschung. He defines here the concept “scientific law” by distinguishing between strictly universal propositions and numerical propositions. Later Popper, drawing upon W. Kneale´s criticism, proposed another definition of natural necessity. He expounds his revised view in Chapter X* of the new appendices of the Logic of Scientific Discovery by means of the famous moa-example. He views statement “All moas die before the age of fifty years” as not physically necessary because its truth depends on the presence of conditions (e.g., impact of a virus) different from singular initial conditions. Ba distinguishing between singular initial conditions and modification conditions I, contrary to Popper, claim that that statement can be viewed as naturally (physically) necessary.