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Structural identification is an essential process in structural health monitoring, condition assessment and structural safety evaluation. This inverse problem becomes more challenging when information on the dynamic loads is missing or not fully known. Hence, it is important to establish methods to identify structural parameters and dynamic loads simultaneously from the measured structural responses which are easy to obtain compared to dynamic loads. This paper proposes a novel method to identify simultaneously structural parameters and dynamic loads from structural responses measured on a limited set of degrees-of-freedom. Firstly, an objective function is defined as the difference between the measured structural responses and the theoretically computed responses, and then the derivative of the residual function with respect to structural parameters is calculated numerically using the forward-difference method. The derivative of the residual function with respect to the external dynamic loads is computed using the state-space formulation and the system matrix composed of Markov parameters to facilitate the derivative-based identification. Secondly, the nonlinear optimization problem is solved using the Levenberg–Marquardt algorithm. Several numerical examples are analysed to demonstrate the effectiveness and robustness of the method. Finally, the effect of initial estimates of the parameters and dynamic loads and the effect of measurement noise, as well as the effects of number of measurements are investigated. The proposed method is also shown to achieve a satisfactory solution even when the initial estimates of parameters and dynamic loads are far from their true values. • The structural parameters and the dynamic loads are identified simultaneously. • A state-space formulation is used to facilitate the identification. • The Levenberg–Marquardt algorithm is used to solve the optimization problem. • The effects of noise, number of measurements and excitations are analysed. [ABSTRACT FROM AUTHOR]