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NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. An investigation of the statistical properties of the mechanics of the dust and gas structures making up the interstellar medium is carried out. The aim is to get a comprehensive picture of the general nature of the motions and structure of the interstellar material that would follow from certain simple assumptions. Comparison with observation then shows to what extent the behavior of the interstellar material can be accounted for on such a basis and to what extent further factors, such as for example magnetic fields, will have to be studied in the hope of finding more satisfactory agreement. In I the interstellar gas is considered. It is shown that the observed radial motions of the gas clouds, if unordered, give too high a kinetic temperature for one to account for the observed clumping of the gas into clouds. The stability of a clump of gas was investigated using a modification of the ideas commonly employed in the virial theorem. It is further shown that given discrete gas clouds, the unordered component of their proper motions must be even lower to prevent them from collapsing into extremely dense structures, possibly clusters of stars, after repeated low velocity collisions. In II the observed dust structures are considered and their general evolution under the influence of the velocity field of the gas and the radiation field is worked out. It is shown that for a continuous distribution of dust sizes, certain types of finely striated structures cannot be formed. From the inadequacies of this non-magnetic theory, one concludes that magnetic fields must play a very significant role in the dynamics of the interstellar medium. Finally, in III the collapse of a nonturbulent nonrotating dust cloud under its own gravitational field is very briefly considered yielding remarkably short collapse times of the order of only [...] years.