Abstract: In this paper, (a) we rerise Theorem 2 of Ref [1] omit the condition V₇>0.(b) we discuss the relative positions of six curves M(s², r)=0, J(s², r)=0, L(s²,r)=0, T(s²,r)=0,s²=s₊² and s²=s_-² Under the condition of the (1.3) distri-butions of limit cycles, we expand the variable regions of parameters (s, r) and clearly. show them in figure, (c) we study the (1, 3) distributions of limit cycles of one kind quadratic systems with two singular points at the infinite: and (d) we give a generalmethod to discuss the (1, 3) distibutions`of limit cycles of system (1.1) whatever there isone, two or three singular points at the infinite.

Key words: eigenfunction expansion variational method, periodic crack, stress intensity factor, T-stress, quadratic system, limit cycle