We talk on some properties of À0-categorical weakly o-minimal structures. Firstly, we present a criterion for goodness of each self-definable subset of an À0-categorical weakly o-minimal structure of convexity rank 1. After that, we give a description of all À0-categorical binary weakly o-minimal theories of convexity rank 1 which generalizes famous result of A. Pillay and Ch. Steinhorn for À0-categorical o-minimal theories [1]. Finally, we present a criterion for holding the Exchange Principle for algebraic closure in an À0-categorical binary weakly o-minimal theory.