Thermoluminescence and thermally stimulated current curves obeying general order kinetics laws are being investigated. For these cases, whose order is not necessarily first or second but rather may have some noninteger value, an effective method of calculating the activation energy is given. This method is based on measuring the temperature at the maximum of the glow peak and the half intensity temperatures. Numerical calculations for orders between 0.7 and 2.5, activation energies between 0.1 and 1.6 eV and frequency factors between 105 and 1013 sec−1 have been done using an I.B.M. 360 computer. The results reveal the general characteristics of these peaks and their dependence on the parameters. The new method for calculating the activation energy is also checked numerically.