In this work, grand canonical Monte Carlo simulations were performed to investigate the adsorption behaviors of three important gases (CO2, CH4 and H-2) in two two-dimensional (2D) covalent organic frameworks (COFs) with different pore sizes. The simulation results show that stepped behavior is common in gas adsorption in 2D COFs, and multi layer formation is likely to be the underlying mechanism. For CO2 adsorption in 2D COFs, stepped phenomena easily occur, and the electrostatic interactions between CO2-CO2 molecules play a dominant role, while, within the temperature range studied, no stepped behaviors were found in isotherms for H-2 adsorption in 2D COFs because of the too weak interactions in the systems. In addition, this work demonstrates that the stepped behaviors are highly affected by temperature, pore size, and the interaction strengths between adsorbates as well as those between adsorbates and adsorbents.