  In this paper the interaction between the shape modes of the wobbling kinks
arising in the family of two-component MSTB scalar field theory models is
studied. The spectrum of the second order small kink fluctuation in this model
has two localized vibrational modes associated to longitudinal and orthogonal
fluctuations with respect to the kink orbit. It has been found that the
excitation of the orthogonal shape mode immediately triggers the longitudinal
one. In the first component channel the kink emits radiation with twice the
orthogonal wobbling frequency (not the longitudinal one as happens in the
$\phi^4$-model). The radiation emitted in the second component has two dominant
frequencies: one is three times the frequency of the orthogonal wobbling mode
and the other is the sum of the frequencies of the longitudinal and orthogonal
vibration modes. This feature is explained analytically using perturbation
expansion theories.
