The integrability conditions and coefficient conditions for the appearance of 5 and 6 limit cycles from the neighborhood of the equator are obtained . an example of cubic system with 6 limit cycles bifurcating from the equator is given for the first time 同时计算出系统的前6个赤道环量,得到了系统在赤道邻域的可积性条件及在赤道附近分支出5个和6个极限环的系数条件,从而首次给出了一个平面三次系统在赤道附近分支出6个极限环的计算实例