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Abstract. This paper describes the construction of second derivative general linear methods in Nordsieck form with stability properties determined by quadratic stability functions. This is achieved by imposing the so-called inherent quadratic stability conditions. After satisfying order and inherent quadratic stability conditions, the remaining free parameters are used to find the methods with L-stable property. Examples of methods with p = q = s = r − 1 up to order four are given.Keywords: stiff differential equations, second derivative methods, Nordsieck methods, inherent quadratic stability, A-and L-stability.