For a positive integer n∈ℕ and a set D⊆ ℕ, the distance graph G_n^D has vertex set { 0,1,…,n-1} and two vertices i and j of G_n^D are adjacent exactly if |j-i|∈D. The condition gcd(D)=1 is necessary for a distance graph G_n^D being connected. Let D={d₁,d₂}⊆ℕ be such that d₁>d₂ and gcd(d₁,d₂)=1. We prove the following results.

• If n is sufficiently large in terms of D, then G_n^D has a Hamiltonian path with endvertices 0 and n-1.
• If d₁d₂ is odd, n is even and sufficiently large in terms of D, then G_n^D has a Hamiltonian cycle.
• If d₁d₂ is even and n is sufficiently large in terms of D, then G_n^D has a Hamiltonian cycle.