Methods for comprehensive structural dynamic analysis generally employ input-output modal analysis with a mathematical model of structural vibration using excitation and response data. Recently operational modal analysis methods using only vibration response data have been developed. In this thesis, both input-output and operational modal analysis, in the presence of significant unmeasured excitations, is considered. This situation arises when a test structure cannot be effectively isolated from ambient excitations or where the operating environment imposes dynamically-important boundary conditions. The limitations of existing deterministic frequency-domain methods are assessed. A novel time-domain estimation algorithm, based on the estimation of a discrete-time autoregressive moving average with exogenous excitation (ARMAX) model, is proposed. It includes a stochastic component to explicitly account for unmeasured excitations and measurement noise. A criterion, based on the sign of modal damping, is incorporated to distinguish vibration modes from spurious modes due to unmeasured excitations and measurement noise, and to identify the most complete set of modal parameters from a group of estimated models. Numerical tests demonstrate that the proposed algorithm effectively identifies vibration modes even with significant unmeasured random and periodic excitations. Random noise is superimposed on response measurements in all tests. Simulated systems with low modal damping, closely spaced modes and high modal damping are considered independently. The accuracy of estimated modal parameters is good except for degreesof- freedom with a low response level but this could be overcome by appropriate placement of excitation and response measurement points. These observations are reflected in experimental tests that include unmeasured periodic excitations over 200% the level of measured excitations, unmeasured random excitations at 90% the level of measured excitations, and the superposition of periodic and random unmeasured excitations. Results indicate advantages of the proposed algorithm over a deterministic frequency domain algorithm. Piezoceramic plates are used for structural excitation in one experimental case and the limitations of distributed excitation for broadband analysis are observed and characterised in terms of actuator geometry and modal deformation. The ARMAX algorithm is extended for use with response measurements exclusively. Numerical and experimental tests demonstrate its performance using time series data and correlation functions calculated from response measurements.