A procedure is discussed for calculating the evolution of a closed system of gas and stars. Numerical and analytical solutions are given for a simple set of prescriptions for the stellar birth rate and the evolutionary end state of stars. The various features of the numerical results are easily understood through the analytic solutions. More significantly, the analytic solutions clearly display how the results will change when the astrophysical input is varied. A fundamental result, which previous investigators have not stressed, is that the metal content Z of the gas in a galaxy need not be a monotonically increasing function of time even if the system is homogeneous in space. We show that under conditions which lead to only a small fraction of mass in the form of gas, there generally may exist an early period with Z much larger than the present value. We propose that the very old super-metal-rich stars under investigation by Spinrad and others could have been formed during such a period.