The rate equations of Er-doped and Yb-Er codoped systems pumped at 0.98 mm are presented, with consideration for the upconversion mechanisms such as cooperative upconversion, cross relaxation, and excited state absorption. A multi-theoretical model is founded to analyze the gain characteristics of Er-doped and Yb-Er co-doped Al2O3 waveguide amplifiers by using rate equations, a two-dimension waveguide finite element model and propagation equations with forward and backward amplified spontaneous emission. The dependence of the gain on amplifier length, pump power and doping concentration is obtained. The optimum design curve is given for designing waveguide amplifiers. The new theory is used to analyze the gain performance of a practical Yb-Er co-doped Al2O3 waveguide amplifier, and the analyzed results are in accordance with the experimental data.