This paper investigates the fault observer design problem for Markovian jump systems with simultaneous time-varying actuator efficiency factors, additive actuator and sensor faults. Two types of adaptive observer methods are developed to solve the investigated design problem. The first one refers an adaptive fault observer, which can reconstruct the states and faults through the online adaptive mechanism. The second one is an iterative adaptive observer, where the iterative mean estimations can approximate to the states, actuator efficiency factors, additive actuator and sensor faults simultaneously. In both two methods, the sliding surface switching problem for jumping systems in sliding mode observer approaches is avoided. Finally, an F-404 aircraft engine system is exploited to demonstrate the effectiveness of the proposed new design techniques. (C) 2019 Elsevier Ltd. All rights reserved.