Bateman and Duquette have characterized Salem numbers in positive characteristic. This work extends their results to 2-Salem numbers from 2-Salem minimal polynomials of the type Y n + λn−1Y n−1 +. .. + λ1Y + λ0 ∈ Fq[X][Y ] where n ≥ 2, λ0 = 0 and deg λn−1 < deg λn−2 = sup i =n−2 deg(λi). The existence of 2-Salem polynomials over Fq, and related questions of irreducibility and algebraicity of 2-Salem numbers, are studied by means of Weiss's method of upper Newton polygons, for q = 2 r , r ≥ 1.