A double hybrid approximation using the Coulomb‐attenuating method (CAM‐DH) is derived within range‐separated density‐functional perturbation theory, in the spirit of a recent work by Cornaton et al. (Phys. Rev. A 2013, 88, 022516). The energy expression recovered through second order is linear in the parameters α and β that control the Coulomb attenuation. The method has been tested within the local density approximation on a small test set consisting of rare‐gas and alkaline‐earth‐metal dimers as well as diatomics with single, double, and triple bonds. In this context, the semiempirical α = 0.19 and β = 0.46 parameters, which were optimized for the hybrid CAM‐B3LYP functional, do not provide accurate interaction and total energies. Using semilocal functionals with density scaling, which was neglected in this work, may lead to different conclusions. Calibration studies on a larger test set would be necessary at this point. This is left for future work. Finally, we propose as a perspective, an alternative CAM‐DH approach that relies on the perturbation expansion of a partially long‐range‐interacting wavefunction. In this case, the energy is not linear anymore in α and β. Work is in progress in this direction. © 2014 Wiley Periodicals, Inc.