The authors study one-step multiderivative methods used in PECE mode to solve initial value problems of the form \(y'=f(x,y),\quad y(x_ 0)=y_ 0,\quad y_ 0\in {\mathbb{R}}^ n.\) In an earlier paper of the authors [BIT 21, 518-527 (1981; Zbl 0474.65052)] intervals of absolute stability were calculated for the single test equation \((1)\quad y'=\lambda y,\quad y(x_ 0)=y_ 0\) in which \(\lambda <0\) was assumed to be real. The multiderivative formulas used as predictors and correctors are found by making approximations to \(e^{\lambda h}\) (h is the constant increment in the independent variable x) in the recurrence relation \((2)\quad y(x+h)=e^{\lambda h} y(x)\) where the solution \(y_{n+1}\) \((n=0,1,2,...,J)\) is determined at the points \(x_ s=sh\) \((s=1,2,...,J)\) by replacing (2) with \(y_{n+1}=R_{m,k}(\lambda h)+O(h^{m+k+1})\) where \(R_{m,k}(\lambda h)\) is the (m,k)-Padé approximation to \(e^{\lambda h}\). In the mentioned earlier paper the authors found that for \(k=1,2,3,4\) the (0,k); (k,0) combinations give the smallest interval of absolute stability when \(\lambda <0\) in (1) is real and that the (0,k); \((m,k^*)\) combinations give the biggest stability interval when \(m=1\) and \(k^*=4\). In the present paper the stability regions for \(\lambda\) complex of all these combinations are determined and plotted. The cited combinations are tested on two problems: the first a system of the form \(y'(x)=Ay(x)\), \(y(0)=y_ 0\), \(y_ 0\in {\mathbb{R}}^ 3\) with complex eigenvalues and the second a system of the form \(y'=f(y)\), \(y(x_ 0)=y_ 0\), \(y_ 0\in {\mathbb{R}}^ 2\) with negative real eigenvalues but a large stiffness ratio.