  We study the cosmological predictions of two recently proposed non-local
modifications of General Relativity. Both models have the same number of
parameters as $\Lambda$CDM, with a mass parameter $m$ replacing the
cosmological constant. We implement the cosmological perturbations of the
non-local models into a modification of the CLASS Boltzmann code, and we make a
full comparison to CMB, BAO and supernova data. We find that the non-local
models fit these datasets as well as $\Lambda$CDM. For both non-local models
parameter estimation using Planck+JLA+BAO data gives a value of $H_0$ higher
than in $\Lambda$CDM, and in better agreement with the values obtained from
local measurements.
