Transverse oscillations of coronal magnetic loops are routinely observed during the space missions. Since the first observation these oscillations were interpreted in terms of kink oscillations of magnetic tubes. Sometimes collective oscillations of two or more coronal loops are observed. This makes the development of theory of collective oscillations of a few parallel magnetic tubes desirable. Another reason for the development of this theory is that there are evidences that at least some coronal loops are not monolithic but consist of many thin magnetic threads. In this paper the linear theory of resonant damping of kink oscillations of two parallel magnetic tubes is developed. Two small parameters, the ratio of the distance between the tubes to the tube length and the ratio of thickness of regions with varying density to the tube radius, are used to obtain the asymptotic expression for the decrement. This expression is calculated explicitly in a particular case of two identical tubes. The dependence of damping time on the separation distance between the tubes and on the density contrast is investigated. In particular, we obtained that the interaction between the tubes reduces the efficiency of resonant absorption.
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