If ε > 0, a subset M of a metric space is said to be ε-connected if for each pair p, q ∈ M there is a finite sequence a0, …, an such that each ai ∈ M, a0 = ρ an = q and the distance from ai−1 to ai is less than ε whenever 0 < i ≦n. It is known [1, p. 117, Satz 1] that a compact metric space is connected if and only if for each ε > 0 it is ε-connected. We present here a proof of an analogous characterization of locally connected unicoherent compacta.