We demonstrate the principle of cavity enhanced absorption with femtosecond modelocked lasers. The wide spectral coverage allowed by these sources makes this a promising high-sensitivity linear absorption technique. The uniformity of the modelocked frequency comb is the feature allowing effective injection of a high finesse cavity. The smooth and stable laser spectral profile guarantees a good background for the intracavity sample absorption spectrum, recorded by a spectrograph and a linear detector array. With a modelocked Ti:Sa laser and a cavity of finesse F 420 (F/pi is the enhancement factor) we obtain a 4nm section of a weak overtone band in 40 ms with 0.2 cm-1resolution,a nd a detection limit of 2x10-7/cm/ radicalHz.