The structural and electronic properties of wurtzite TlxIn1-xN materials have been investigated from first principles within the density functional theory (DFT). Band structures were obtained with the modified Berke-Johnson (MBJLDA) approach. A narrow band gap of 63 meV, induced by a strong spin-orbit coupling, is predicted in the hypothetical thallium nitride. The band gap inversion in TIN suggests that this compound is a promising candidate for a topological insulator. The lattice parameters of TlxIn1-xN alloys exhibit a linear behavior as a function of a TI content x. An incorporation of Ti atoms in these systems leads also to a linear decrease of a band gap. For x>0.3 a very narrow energy gap, analogous to that of the pure TIN, is revealed. The band gap reduction of 26 meV/%71 is comparable in value to those reported in the literature for dilute Bi-doped GaSb and InSb. The Tl-doped InN systems are promising materials for infrared optoelectronic devices. (C) 2017 Elsevier B.V. All rights reserved.