Abstract: Using phase-plane method,a variety of analytic solutions are obtained through solving free p coordinate equations without introducing kdv equation.The structures,existing conditions,and moving features of the air motions expressed by the analytic solutions are discassed.Results show that,for the weak high or low pressure systems at their first stage of development,their structures,existing conditions and moving features are influnced commonly by atmospheric static stability,heating of latent heat of conclensation,and surface sensible heating.