Substitutions of constant length on two symbols and their corresponding minimal dynamical systems are divided into three classes: finite, discrete and continuous. Finite substitutions give rise to uninteresting systems. Discrete substitutions yield strictly ergodic systems with discrete spectra, whose topological structure is determined precisely. Continuous substitutions yield strictly ergodic systems with partly continuous and partly discrete spectra, whose topological structure is studied by means of an associated discrete substitution. Topological and measure-theoretic isomorphisms are studied for discrete and continuous substitutions, and a complete topological invariant, the normal form of a substitution, is given. 0. Introduction. Let 0 denote a substitution of constant length n on the symbols 0 and 1. Our main objective is the classification of the dynamical systems (0,, r) arising from such substitutions. A substitution 0 is either finite, discrete, or continuous as defined in ?3. Finite substitutions give rise to dynamical systems all of whose minimal sets are periodic orbits. Discrete and continuous substitutions both give rise to strictly ergodic dynamical systems with discrete and partially continuous spectra respectively. More specifically, if 0 is discrete, then V. is the orbit-closure of a Toeplitz bisequence, and if 0 is continuous, then (C is the orbit-closure of an extended generalized Morse sequence. Dynamical systems belonging to discrete substitutions are measure-theoretically isomorphic if and only if the lengths of the substitutions have the same prime factors. If 0 is discrete, we are able to give an explicit construction of (0,, r) as an almost one-to-one extension of the n-adic system (Z(n), r). We associate with 0 an object called a group system which is a complete invariant for topological isomorphism of (0,, r). The concept of normal form for a discrete substitution is defined and it is shown that discrete substitutions of the same length possess topologically isomorphic dynamical systems if and only if they have the same normal form. To each continuous substitution 0 we associate a discrete substitution 0 of the same length such that (0, r) is a distal extension of (06, r). Each fibre consists of two points which are mirror images of each other. A normal form for continuous Received by the editors May 22, 1970. AMS 1970 subject classifications. Primary 28A65, 54H20.