A method is developed for determining the nonlinear stiffness and damping characteristics of structures subjected to crash loading environments. The system identification is accomplished using adaptive time domain, constrained minimization techniques. The underlying assumptions are that the stiffness and damping characteristics of a structural element are separable, that the characteristics can be idealized with piecewise linear segments, and that the equations of motion resulting from the above idealizations can be considered quasilinear. Incremental equations of motion, including error terms, are formulated and solved for nonnegative parameters using linear and quadratic programming algorithms. The parameters are estimated using three formulations--minimizing the sum of the absolute errors (L₁ error norm), minimizing the sum of the squared errors (L₂ error norm), and minimizing the maximum absolute error (L_∞ error norm). Adaptivity is incorporated into the formulation for identifying discontinuities in the structural characteristics and for improving the parameter estimation. Finally, the methodology allows for the specification of upper and lower bounds for the damping forces and allows for relaxing the requirement of nonnegativity of the parameters. The adaptive formulation and the specification of the constraints are shown to be the key elements leading to the identification of the characteristics of the nonlinear structures. The results obtained from the L1 and L2 error norm formulations consistently provided the best agreement to known model characteristics. The motivation for this research is the need to identify the structural parameters for lumped mass models of automobiles, using acceleration and barrier load data collected during frontal barrier crash testing.