Abstarct: In this thesis, an analytic and numerical solution of the initial value problems of non-causal delay linear differential equations is considered. In general, it is possible that the corresponding initial value problem of a non-causal DDAE possesses a unique solution, even though the associated DAE is neither square nor uniquely solvable. Such non-square systems arise in many applications, in particular for dynamical systems which are automatically generated by modeling and simulation software, due to redundant conditions and equations may make the resulting system over- or under-determined. The numerical solution of these equations with numerical methods such as Rang-Kuta or a backward difference formula may not be correct, therefore, in order for numerical methods to be applied to these equations well, these types of equations must be regulated in order to allow for regularized equations Solved with any numerical method. In the following, we introduce the derivative index for set over- or under-determined, which is called the Strangeness index, and we use it for the under-determined algebraic differential equations, and we will use the notion of Strangeness index for delayed linear algebraic differential equations, and we obtain the compatibility, smooth and uniqueness conditions of the device's solvability using this index. In the end, we solve two types of neutral and delayed equations non-causal delay linear differential algebraic respectively analytically and numerically.