Lower-flow regime sand waves emerge from flat sand beds under steady uniform flow conditions. The time variation of the sand-wavelet height and length from inception to equilibrium are derived from linear and nonlinear ordinary differential equation models. The nonlinear model predicts more reasonably time variations of the bed-form length than the linear model. The results of the model are supported by the laboratory experimental data of Bishop in 1977 and Melville and Coleman in 1994.