A constructive algorithm is proposed and illustrated for parametric estimation in delayed nonlinear time-varying dynamic system models from available data. The algorithm uses Chebyshev spectral collocation and optimization. The problems addressed are estimations with complete state vector and incomplete state vector availability. Using an equivalent algebraic description of dynamical systems by Chebyshev spectral collocation and data, a standard least-squares residual cost function is set up for complete and incomplete information cases. Minimization of this cost yields the unique solution for the unknown parameters for estimation with complete state availability, only owing to the fact that the cost function is quadratic and positive definite. Such arguments cannot be made for estimation with incomplete state availability as the cost function is positive definite albeit a nonlinear function of the unknown parameters and states. All the algorithms are presented stepwise and are illustrated using suitable examples.