I kinetic equations for the theory of monatomic rarefied gases were derived in Ref. 1. A modification of these equations for the case in which a constant field of gravitational forces is present is given in Ref. 2. The present paper investigates this problem in a considerably more general aspect than do Refs. 1 and 2; the form of integral kinetic equations is established for a mixture of monatomic gases in which chemical reactions may occur during motion and in which motion occurs in a constant external field of gravitational forces. As in Refs. 1 and 2 it is assumed that only paired collisions of molecules are important for the motion of the gas. This excludes such chemical reactions from the investigation which may occur only for multiple (triple, etc.) collision of gaseous molecules. The equations that will be derived are not applicable to the investigation of the motion of gases in which reactions of this kind take place. In addition, it is assumed that the gas particles formed during the chemical reactions are electrically neutral; the Coulomb interaction, which should be taken into consideration for charged gas particles, is neglected. This assumption means that the derived equations are not suitable for an investigation of the motion of gases in the presence of considerable ionization. The notations from Refs. 1 and 2 are used, since the investigation concerns quantities which have the same physical meaning. The state of the mixture of gases with internal degrees of freedom cannot be described by one distribution function /(f, u, t) as was the case in Refs. I and 2 for the investigation of monatomic gases without internal degrees of freedom. Representation of the state of a mixture of gases with internal degrees of freedom requires a system of distribution functions. First of all, one has gas particles of different kinds. The type of gas particle can be indicated with an index that assumes a certain finite number of values. In addition, gas particles of a certain kind can be in different energy states that can be denoted by a finite set of quantum numbers (indices), each of which may pass through a finite or denumerable sequence of values.* In general, one is concerned with a finite or denumerable aggregate of types and states of gas particles; in the following it is convenient to disregard the differences between the types of gas particles and their different energy states and consider only aggregate types of gases. Let us then employ such a representation of the types of gas particles and enumerate with index i the types of particles in terms of the expanded concept. In such a case, the state of the gas can be described by a finite or denumerable set of distribution f unctions/i(f, u, t). The object of the present paper is to construct a complete system of integral equations from which functions /»• can be derived.