We analyze the null controllability properties from the exterior of two parabolic-elliptic coupled systems governed by the fractional Laplacian (−d2 x)s, s ∈ (0,1), in one space dimension. In each system, the control is located on a non-empty open set of R\(0,1). Using the spectral theory of the fractional Laplacian and a unique continuation principle for the dual equation, we show that the problem is null controllable if and only if 1/2 < s < 1. .