This paper presents a theoretical framework in which one can discuss the mass spectra of interacting species. It is applied here to interstellar neutral hydrogen clouds. The theory predicts the number of objects of mass m per unit volume at time t , N ( m , t ). An equation for |$\partial N (m, t)/\partial t$| is derived similar to the Boltzmann equation. Included in the kernel of the double integral, in addition to |$\sigma v$| is the central physical element of the theory, the conditional probability that once objects of mass m, m ′ have collided they yield new objects of mass M, M ′, . . . , M ″. This quantity is symbolized by P ( m , m ′; M , M ′, . . . , M ″). The mathematical structure of the system has been investigated and the results depend on the satisfaction of mass conservation, i.e. |$\frac {d}{dt}\int mN(m, t)\enspace {dm} = 0$| . If there is mass conservation then the equilibrium solution |$\partial N/ \partial t = 0$| for all m ) exists, is unique, and is stable relative to small perturbations. In addition, in these circumstances, every solution of the time dependent problem decays, exponentially, to the equilibrium solution independently of the initial conditions (i.e. N ( m , 0)). If there is no mass conservation, no equilibrium solution can exist and the result of a time integration depends explicitly on N ( m , 0). We have constructed models for P based on both probabilistic considerations and the best available physics. Both three-dimensional (spheres) and two-dimensional (aligned right circular cylinders) calculations have been made with and without kinetic energy equipartition (KEE). The observational data indicate that the simple analytical form of a power law |$(N(m) \approx m^{-Y}$)| adequately describe the data with Y near 2. The model independent effect of KEE is to flatten the calculated mass spectra by approximately −0.2 in Y . As the simple case of total coalescence and uniform |$\sigma v$| can be studied, in all aspects, completely analytically, it forms a background for the discussion of more complex models. The results of the theory for H I clouds are encouraging in that a statistical model of this nature, with sufficiently realistic P , can not only account for the observed, relatively flat, spectra in general, but have the capability of describing more complex distributions. For the theory to be viable the fragmentation of even non-gravitationally bound clouds must almost never occur. We have assumed the stability of such objects in the numerical calculations only for a time long compared to a collision time ( |$\approx 3 \times 10^5 \text {yr}$| ). The approximate existence of pressure equilibrium between H I clouds and the intercloud region is our theoretical justification of this. A short summary of a similar hypothesis in regard to the asteroid belt is given.