We investigate topological mixing for ℤ and ℝ actions associated with primitive substitutions on two letters. The characterization is complete if the second eigenvalue θ2 of the substitution matrix satisfies |θ2| ≠ 1. If |θ2|, then (as is well known) the substitution system is not topologically weak mixing, so it is not topologically mixing. We prove that if |θ2| > 1, then topological mixing is equivalent to topological weak mixing, which has an explicit arithmetic characterization. The case |θ2| = 1 is more delicate, and we only obtain some partial results.