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We consider systems of quasi-periodic linear differential equations associated to a ‘resonant’ frequency vector 
${\it\omega}$, namely, a vector whose coordinates are not linearly independent over 
$\mathbb{Z}$. We give sufficient conditions that ensure that a small analytic perturbation of a constant system is analytically conjugate to a ‘resonant cocycle’. We also apply our results to the non-resonant case: we obtain sufficient conditions for reducibility.
