Development of dynamic state estimation techniques and their applications in problems of identification in structural engineering have been taken up. The thrust of the study has been the identification of structural systems that exhibit nonlinear behavior, mainly in the form of constitutive and geometric nonlinearities. Methods encompassing both linearization based strategies and those involving nonlinear filtering have been explored. The applications of derivative-free locally transversal linearization (LTL) and multi-step transversal linearization (MTrL) schemes for developing newer forms of the extended Kalman filter (EKF) algorithm have been explored. Apart from the inherent advantages of these methods in avoiding gradient calculations, the study also demonstrates their superior numerical accuracy and considerably less sensitivity to the choice of step sizes. The range of numerical illustrations covers SDOF as well as MDOF oscillators with time-invariant parameters and those with discontinuous temporal variations. A new form of the sequential importance sampling (SIS) filter is developed which explores the scope of the existing SIS filters to cover nonlinear measurement equations and more general forms of noise involving multiplicative and (or) Gaussian/ non-Gaussian noises. The formulation of this method involves Ito-Taylor’s expansions of the nonlinear functions in the measurement equation and the development of the ideal ispdf while accounting for the non-Gaussian terms appearing in the governing equation. Numerical illustrations on parameter identification of a few nonlinear oscillators and a geometrically nonlinear Euler–Bernoulli beam reveal a remarkably improved performance of the proposed methods over one of the best known algorithms, i.e. the unscented particle filter. The study demonstrates the applicability of diverse range of mathematical tools including Magnus’ functional expansions, theory of SDE-s, Ito-Taylor’s expansions and simulation and characterization of the non-Gaussian random variables to the problem of nonlinear structural system identification.