Using the full-potential local orbital minimum-basis method, we have performed a systematic investigations on the electronic, structural, and magnetic properties related to shape memory applications for Ti2CoX (X=Al, Ga, In) alloys. Our results confirm that these alloys are half-metallic ferromagnets with total magnetic moment of 2 mu(B) per formula unit in austenite phase, and undergo a martensitic transformation at low temperatures. The relative stabilities of the martensitic phases differ considerably between Ti2CoX (X=Al, Ga, In). Details of the electronic structures suggest that the differences in hybridizations between the magnetic components are responsible for trends of phase. Quantitative estimates for the energetics and the magnetizations indicate that Ti2CoGa is a promising candidate for shape memory applications. (C) 2014 Elsevier Ltd. All rights reserved.