The quantum theory of two-level atom single-mode laser system of Sargent, Scully and Lamb is extended to two-mode laser in a three-level atomio system with common lower level, and master equation is obtained for the system, with all the three levels being pumped. There appear four terms in the master equation that are absent in the single-mode case and those interpreted as 2-photon processes play an especial role in the present case. The master equation is represented by a probability flow diagram in two-dimensions with the photon numbers nx and % of the two-mode as variables. The probability flow diagram can be extended to infinity, and. each arrow of it represents a term of the right hand side of master equation. By taking sum over one of the variables rix or n2> the master equation is reduced to two equations, each of them can be represented by an one-dimensional probability flow diagram. The equation of motion under steady state is obtained by considering the correspondence between the macrosoopio balance and the microscopic balance. A parameter H is introduced to reduoe the equation of motion and to facilitate the mathematical procedure and a formal solution is thus obtained. Using the equation of motion and its formal solution various operation characteristics are discussed. Among them are: the threshold condition for each mode; the condition of only one mode operation; the variation of photon statistics between single-mode operation and two-mode operation and the variation of photon statistics with lower level being pumped and not pumped.