In This Article, the Applications of the New Haar Wavelet Collocation Methods Called as Haar Wavelet Collocation Method (HWCM) and Higher-Order Haar Wavelet Collocation Method (H-HWCM) Are Developed for the Solution of Linear and Nonlinear Systems of Ordinary Differential Equations. the Proposed H-HWCM is Compared with a Variety of Other Methods Including the Well-Known HWCM. the Quasi-Linearization Technique is Introduced in the Nonlinear Cases. the Stability and Convergence of Both Techniques is Studied in Detail, Which Are the Important Parts to Analyze the Proposed Methods. the Efficiency of the Methods is Illustrated with Certain Numerical Examples, But the H-HWCM is More Accurate with Faster Convergence Than the HWCM and Other Methods Reported in the Literature.