We present experimental and finite-difference time-domain simulation results on the tunability of optical resonant modes of spiral microtube cavities, rolled-up from square patterned SiO/SiO(2) thin nanomembranes on glass substrates. The peak positions of resonant TM modes shift to lower energies by coating the microtube wall with Al(2)O(3) monolayers, which is well described by simulations. Moreover, a second group of tunable resonant modes appears beyond a certain critical thickness of the coated Al(2)O(3). The polarization of this group of modes is TE, as we find out by a detailed analysis of the polarization-dependent photoluminescence spectra.