The purpose of this paper is to give the classification of the excluded minors for classes of matroids. Theorem 1.1: The excluded minors for the class of matroids that are binary or ternary are \(U_{2,5}\), \(U_{3,5}\), \(U_{2,4}\oplus F_{7}\), \(U_{2,4}\oplus F_{7}^{*}\), \(U_{2,4}{\oplus}_{2} F_{7}\), \(U_{2,4}{\oplus}_{2} F_{7}^{*}\), and the unique matroids obtained by relaxing a circuit-hyperplane in either \(AG(3,2)\) or \(T_{12}\). The technique is matroid-theoretic and graph-theoretic, involving results from the book and a paper by \textit{J. G. Oxley} [Matroid theory. Oxford: Oxford University Press (1992; Zbl 0784.05002); ``On the interplay between graphs and matroids,'' Lond. Math. Soc. Lect. Note Ser. 288, 199--239 (2001; Zbl 0979.05030)] and results on the structure of almost-regular matroids by \textit{K. Truemper} [``A decomposition theory for matroids. VI: Almost regular matroids,'' J. Comb. Theory, Ser. B 55, No. 2, 253--301 (1992; Zbl 0809.05024)], and leads to a finite task. A number of propositions related with excluded minors that have low rank, corank or connectivity as well as excluded minors with at most nine elements are established. These results show that authors can restrict their attention to 3-connected excluded minors with rank and corank at least four and with at least ten elements and are then utilized to prove Theorem 5.1 on producing such excluded minors by relaxing a circuit-hyperplane in a binary matroid. Let \(\mathcal M\) be a class of matroids that are either binary or ternary. The authors prove Theorem 6.1 and Proposition 6.2 concerning a connection between the excluded minors of \(\mathcal M\) and Truemper's class of almost-regular matroids. After the reduction to a finite list of excluded minors the authors conclude with a proof of their principal result. A number of examples and figures are provided to illustrate the basic theorems. There is a bibliography of 31 items.