We present a model and a simple-to-implement numerical procedure that obtains the normal detonation shock velocity (D-n)-curvature (kappa) relationships for an explosive material with nonideal equation of state and an arbitrary reaction rate law. In addition we illustrate numerically (for a nonideal equation of state) and analytically (for an ideal equation of state with a large activation energy rate law) that for sufficient rate-state-sensitive explosives, the corresponding D-n, kappa-response curve can have two turning points, at D-n, kappa,-pairs [(D-n)(1), kappa(1)], [(D-n)(2), kappa(2)], such that kappa(1) > kappa(2) > 0 for D-CJ greater than or equal to (D-n)(1) greater than or equal to (D-n)(2), and such that the curve has a Z-shape. The top branch of the Z response curve has been previously associated with detonation extinction at a critical curvature. The bottom branch can be possibly associated with low-velocity detonation and rapid change from low-order detonation to high-order.