This thesis is devoted to the development of new approaches for control coordination of PSSs (power system stabilisers) and FACTS (flexible alternating current transmission system) devices for achieving and enhancing small-disturbance stability in multi-machine power systems. The key objectives of the research reported in the thesis are, through optimal control coordination of PSSs and/or FACTS devices, those of maintaining satisfactory power oscillation damping and secure system operation when the power system is subject to persisting disturbances in the form of load demand fluctuations and switching control. Although occurring less frequently, fault disturbances are also considered in the assessment of the control coordination performance. Based on the constrained optimisation method in which the eigenvalue-based objective function is minimised to identify the optimal parameters of power system damping controllers, the thesis first develops a procedure for designing the control coordination of PSSs and FACTS devices controllers. The eigenvalue-eigenvector equations associated with the selected electromechanical modes form a set of equality constraints in the optimisation. The key advance of the procedure is that there is no need for any special software system for eigenvalue calculations, and the use of sparse Jacobian matrix for forming the eigenvalue-eigenvector equations leads to the sparsity formulation which is essential for large power systems. Inequality constraints include those for imposing bounds on the controller parameters. Constraints which guarantee that the modes are distinct ones are derived and incorporated in the control coordination formulation, using the property that eigenvectors associated with distinct modes are linearly independent. The robustness of the controllers is achieved very directly through extending the sets of equality constraints and inequality constraints in relation to selected eigenvalues and eigenvectors associated with the state matrices of power systems with loading conditions and/or network configurations different from that of the base case. On recognising that the fixed-parameter controllers, even when designed with optimal control coordination, have an inherent limitation which precludes optimal system damping for each and every possible system operating condition, the second part of ii the research has a focus on adaptive control techniques and their applications to power system controllers. In this context, the thesis reports the development of a new design procedure for online control coordination which leads to adaptive PSSs and/or supplementary damping controllers (SDCs) of FACTS devices for enhancing the stability of the electromechanical modes in a multi-machine power system. The controller parameters are adaptive to the changes in system operating condition and/or configuration. Central to the design is the use of a neural network synthesised to give in its output layer the optimal controller parameters adaptive to system operating condition and configuration. A novel feature of the neural adaptive controller is that of representing the system configuration by a reduced nodal impedance matrix which is input to the neural network.