A theoretical investigation of the dynamic response of a pair of interacting carbon nanotubes (CNTs) dispersed in a liquid medium under the presence of an alternating current (AC) electric field is presented. The proposed modeling strategy is based on the dielectrophoretic (DEP) theory and classical electrodynamics, and considers the effect of an applied AC electric field on the rotational and translation motion of interacting CNTs represented as electrical dipoles. The mutual interaction between a pair of adjacent CNTs stems from the presence of DEP-induced charges on the CNTs and, as such, contributes to the rotational and translational dynamics of the system. Based on experimental evidence, the parameters which are expected to cause a major contribution to the CNTs motion are investigated for different initial configurations. Based on the obtained results, it is here predicted that high electric field frequencies, long CNTs, high values of electrical permittivity and conductivity of CNTs immersed in solvents of high polarity promote faster rotational and translational motion and therefore faster equilibrium conditions (CNT tip-to-tip contact and horizontal alignment). The results incorporate important knowledge towards a better understanding of the complex mechanisms involved in the efforts of tailoring CNT networks by electric fields.