We study the evolution of two planets around a star , in mean-motion resonance and undergoing tidal effect .
We derive an integrable analytical model of mean-motion resonances of any order which reproduce the main features of the resonant dynamics .
Using this simplified model , we obtain a criterion showing that depending on the balance of the tidal dissipation in both planets , their final period ratio may stay at the resonant value , increase above , or decrease below the resonant value .

Applying this criterion to the two inner planets orbiting GJ~163 , we deduce that the current period ratio ( 2.97 ) could be the outcome of dissipation in the 3:1 MMR provided that the innermost planet is gaseous ( slow dissipation ) while the second one is rocky ( faster dissipation ) .
We perform N-body simulations with tidal dissipation to confirm the results of our analytical model .

We also apply our criterion on GJ~581 b , c ( 5:2 MMR ) and reproduce the current period ratio ( 2.4 ) if the inner planet is gaseous and the outer is rocky ( as for GJ~163 ) .

Finally , we apply our model to the Kepler mission ’ s statistics .
We show that the excess of planets pairs close to first order MMR but in external circulation , i.e. , with period ratios P _ { out } / P _ { in } > ( p + 1 ) / p for the resonance ( p + 1 ) : p , can be reproduced by tidal dissipation in the inner planet .
There is no need for any other dissipative mechanism , provided that these systems left the resonance with non-negligible eccentricities .