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In this paper we shall prove two theorems: Firstly, a minimal flow is regularly almost periodic if and only if it is almost automorphic and the dimension of the set of eigenvalues is 1. Secondly, a minimal flow is pointwise regularly almost periodic if and only if it is equicontinuous and the dimension of the set of eigenvalues is 1.

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Let Bv be the set of real valued functions on R which are bounded and uniformly continuous. For /, g € Brj , put rf

Abstract.Let Bv be the set of real valued functions on R which are bounded and uniformly continuous. For /, g € Brj , put rf 0 there exists a S > 0 such that for x, y £ X with dxix, y) < ô and t £ R we have dxiTix, t), P(y, t)) < e. Proposition 1. Let T be a flow on a compact metric space X. If T is equicontinuous, then for every x £ X CTix) is a minimal set of T.Proof. Easy.Let Tn be flows on I" (zz = 1, 2, ...). We denote the product flow of {Tn} on Y\ZxXn by n~i Tn ■