The H-infinity control problem of general preview/delayed systems is solved using analytic solutions of the corresponding operator Riccati equations. The solution to the problem can be applied to a broad range of input/output delayed systems and enables the handling of preview/delayed control problems. The solvability condition is characterized by the roots of the transcendental equations and the control law for the general problem is given based on a predictive compensation with an integro-differential observer. Some interpretations of typical control problems are presented based on the solvability condition and the resulting control law.