The artificial intelligence (AI)-based weather models have shown great promise for weather forecasts. But they rely on the initial conditions provided by traditional paradigm of numerical weather prediction, which has a cycled data assimilation (DA) to combine short-term forecasts and observations. This study demonstrates the ability of AI weather models within the framework of cycling DA, achieving a successful and stable cycling DA with assimilation of real-time sounding observations. For FengWu, assimilation of wind observations can better constrain the atmospheric state than assimilation of temperature observations, and both produce more accurate analyses and 6-h forecasts than assimilation of specific humidity observations. But when Pangu-Weather is applied, assimilating wind observations cannot constrain the state variables of temperature and specific humidity as well as that with FengWu. This indicates that the influences of observation types on cycling DA with AI weather models are model-dependent, associated with the intrinsic error characteristics.