Abstract:  According to   algebraic stability and (k,p,q)-algebraic stability of general linear methods, the algebraic conditions of mumerical stability of θ-one-leg methods are obtained,i.e.,θ-one-leg methods is  algebraically  stable and diagonally stable under the constraint  θ≥1/2,and  θ-one-leg methods is  (1,0,2θ -1-ε)-algebraically  stable for any constant ε ≥ 0.

Key words: &theta, -one-leg methods；general linear methods；algebraic stability；diagonal stability