The general aim of this thesis is to use the new processes and methods to estimate the parameters in problems which are described by ordinary differential equations. This thesis is a try to connect the applicable side of these problems with the mathematical methods to estimate their parameters The following is some of what have been achieved in this thesis: 1. Classification of the mathematical model of these problems. 2.Treatment of nonuniquenees trouble for one of the best methods in this subject (Least squares method) for some problems using Chebyshev apprpximation method and checking this method on cases study. 3.Construction of an algorithm which is called Chebyshev approximation for parameter estimation in ordinary differential equation algorithm and introducins a good description of it and support this description by theorems. 4.Description and derivation for one of the important algorithms of recursive estimation methods, extended Kalman estimator algorithm which depends on statistical manner. Also the derivation of recursive Least squares method will be introduced in this thesis. 5. Derivation and description of important formulas to convert some models from continuous case to discrete case (as conversion of continuous case of Gauss Markov model to discrete Gauss Markov model) and other conversions. This conversion is important in this subject because it makes these models suitable to treat by these algorithms 6. Discussion of advantages and disadvantages of these algorithms and introducing some conclusions about their results. 7. Derivation of statistic test to test the error innovation in extended Kalman estimator algorithm and calculation of ihe confidence interval for the mean of this error. 8. All procedures and algorithms are constructed and rogrammed on (Mathcad Plus 6.0 (1995) and Matlab ver.4.2.c.l (1994)) Packages. And some of these procedures will be illustrated for some cases. These Packages are important to obtain more accurate results, they assist to construct any algorithm with less labor and in a simpler form, also, they save many mathematical facilities to solve complex problems. 9. The applications of this subject are very wide, some of them are chosen in this thesis to be cases study as tracking problems (tracking of radiant source from a moving aircraft on 2-dirnensionai plan, tracking of falling body problem, tracking of aircraft using polar-coordinates model problem, tracking of aircraft using 3-dimensional model problem), the growth problem for_a simple case, and a chemical problem to show importance of this subject in the chemical applications. The mathematical models for these problems are described by a simple form, they are illustrated by figures to illustrate the meaning and position of the parameters in these models, also, the results are illustrated and simulated by animation figures.