Creep buckling of columns is analyzed for materials obeying nonlinear single memory integral constitutive laws. There have been two basic methods to analyze creep buckling of columns; the Rabotnov and Shesterikov's linearized dynamical approach and Hoff's quasistatic nonlinear approach, the former predicts critical buckling loads and the latter yields critical buckling times. The two theories are generally believed to be independent of each other. Through investigation of creep phenomena other than steady creep, the two different creep stability criteria are found to be correlated and thus the linear treatment is justified by a nonlinear approach. It is also shown that the Hoff approach can be used to derive critical creep buckling loads. The missing link between the two theories is found in this paper.