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We investigate the linearized equations of motion in three dimensional Born-Infeld gravity theory. Motivated by this model, we calculate the quasinormal modes of BTZblack hole solutions of parity-even gravity theories in three dimensions by using numericalmethods. The results are classi ed in three families and they are so accurate such thatit allows us to propose analytical form for the quasinormal frequencies. We nd newquasinormal modes which have been missing in the literature of the analytical studiesof three dimensional massive gravitons. These new modes do not have the known towerstructure and they are purely imaginary for any value of the angular momenta. Consideringthe complete set of the quasinormal modes, we show that the BTZ black hole solutions areunstable for any value of the parameters of the theory. We con rm our numerical resultsby computing the new eigenmodes analytically at zero angular momentum
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