For a state-space time-delay system with linearly coupled input and output disturbances, a simultaneous state and disturbance estimation technique is developed. For a nonlinear state-space time-delay system with dependent input and output disturbances, a nonlinear estimator is also proposed to estimate system state and disturbance at the same time. The proposed estimator techniques are applied next to estimate system state and fault signal. Via actuator and/or sensor signal compensation, a simple and efficient fault-tolerant operation can be realized. In the developed design, no limitations and prior knowledge are required on the considered faults. Moreover, identical actuator and/or sensor switches and control gain reconstruction are not necessary. Therefore, the proposed estimation and fault-tolerant scheme is economical and convenient in practical applications. After that, the design techniques are extended to the case of systems with a class of uncoupled input and output faults. Examples and simulations given show excellent signal estimation and fault-tolerant performance.