Inspired by the work of Amitsur [1] on finite groups whose irreducible characters all have degree (multiplicity) 1 or 2, in this paper we study association schemes whose irreducible characters all have multiplicity 1 or 2. We will first show that the general case can be reduced to commutative association schemes. Then for commutative association schemes with multiplicities 1 or 2, we prove that their Krein parameters are all rational integers. Using automorphism groups of association schemes, we obtain a characterization and classification of those commutative association schemes all valencies and multiplicities of which are 1 or 2 in terms of Cayley schemes.

受 Amitsur [1] 对不可约特征都具有度数（重数）为 1 或 2 的有限群的工作启发，本文研究了其不可约特征都具有多重性 1 或 2 的关联方案。我们将首先证明一般情况可以简化为交换关联方案。然后对于重数为 1 或 2 的交换关联方案，我们证明它们的 Kerin 参数都是有理整数。使用关联方案的自同构群，我们获得了那些交换关联方案的特征和分类，根据凯莱方案，这些可交换关联方案的效价和重数均为 1 或 2。