The flow characteristics of the transitional oscillatory flows are investigated analytically and experimentally in the entrance region of a square duct. The systems of conservation equations are analytically solved by linearizing the non-linear convective terms for the developing transitional oscillatory flows in a square duct. The analytical solutions are obtained in the form of infinite series for the velocity profiles. The experimental study for the air flow in a square duct is carried out to measure the velocity profiles and waveforms by using a hot-wire anemometer with the data acquisition and processing systems. The theoretical and experimental results provide the major characteristics of the developing transitional oscillatory flows, such as velocity profiles, velocity waveforms, and entrance length. The velocity profiles in the decelerating phase are larger than those in the accelerating phase for the developing transitional oscillatory flows. The correlations of the entrance length of the transitional oscillatory flows in a square duct are found to be $Le/Dh=K{cdot}Re_{os}/2({omega}^+)^2$, where K is 1.23 of an experimental constant.