We have performed first-principles density functional theory calculations within generalized-gradient approximation to obtain the structural, mechanical, electronic, and dynamic properties of Tin+1GaNn compounds. In order to examine the stability of these compounds, formation enthalpies, single-crystal elastic constants, and phonon dispersion curves were calculated. We show that all compounds are stable, while alpha-Ti4GaN3 is the most stable. The density of states calculations also demonstrate that all of the compounds are metallic. Additionally, bonding nature and related characteristics such as Mulliken atomic charges and bond overlap populations were investigated. Furthermore, thermodynamic properties were calculated by means of phonon dispersion curves. The results are compared in this work with available experimental values and theoretical calculations.