The formalism of Schramm and Wasserburg (1970) for determining the mean age of the elements is extended. Modelindependent constraints (constraints that are independent of a specific form for the effective nucleosynthesis rate and Galsct,ic chemical evolution over time) are derived on the first four terms in the expansion giving the mean age of the elements, and from these constraints limits are derived on the total duration of nucleosynthesis. These limits require only input of the Schramm-Wasserburg parameter Aand of the ratio of the mean time for formation of the elements to the total duration of nucleosynthesis, t,/T. The former quantity is a function of nuclear input parameters. Limits on the latter are obtained from constraints on the relative rate of nucleosynthesis derived from the ZSZTh/W%, 2sU/"8U, and shortere Op~ral~d by Unlversltles Research Association Inc. under contract with the United States Department 01 Energy-2lived chronometric pairs. Beca.use lBTRe may decay faster in hot stars than in interstella,r space, its effective lifetime may be less than the laboratory value; thus, using the laboratory decay rate gives an upper limit on Am for the '87Re/'mOs pair, which gives an upper limit on t,he duration of nucleosynthesis. A lower limit on A-can be determined from the n2Th/258U pair, which then yields a lower limit on the duration of nucleosynthesis. The results found are that the eJective nucieosynthesis rate was relatively constant over most of the duration of nucleosynthesis and that 0.43 5 t,/~c 0.5% From these constraints on t,/T, a nearly modelindependent range for T,,, the age of the Galaxy, is obtained: 8.7 Gyr C TGd s 28.1 Gyr. Improvements in nuclear and meteoritic data could lead to a dramatic narrowing of this model-independent range in the near future. Detailed Galaxy evolution models give a fa.r na,rrower ra.nge on t,he age, but t,he results depend on assumptions about t.he specific form of the effective nucleosynthesis ra.te.