Joint estimation of states and parameters in state-space systems is usually realized with adaptive observers. For continuous time state-space systems, adaptive observers are generally in the form of ordinary differential equations. The implementation of such an adaptive observer requires the simultaneous solution of the differential equations for both state and parameter estimations. This chapter presents an alternative approach which decomposes state and parameter estimations in several steps. Each algorithm designed with this approach is also a system of ordinary differential equations, but with the particularity of being block-triangular so that state and parameter estimations are decoupled. The resulting stepwise solution is numerically more efficient. This new approach is applicable to multiple-input multiple-output linear time varying systems.