Self-diffusion in liquid and solid alloys of the Ti-Al system, including pure Ti and Al metals, is investigated using the molecular dynamics method. Apart from intermetallides Ti3Al, TiAl, and TiAl3, disordered alloys with analogous ratios of the components are considered. For these systems, self-diffusion characteristics are obtained separately for Ti and Al atoms. According to obtained results, the diffusion activation energy of both liquid and solid alloys of the Ti-Al system considerably depends on the concentration of components, repeating approximately the phase diagram. The activation energy of disordered alloys turns out to be smaller by 1.5 times than that for ordered alloys. No appreciable difference in the diffusion mobilities of atoms of different species is detected in analysis of self-diffusion in melts and in solid disordered alloys. However, in the case of ordered alloys (especially intermetallides Ti3Al and TiAl), this difference is manifested clearly: Al atoms diffuse much more slowly than Ti atoms. Diffusion in intermetallide TiAl3 is anisotropic: main displacements of atoms occur along atomic planes with alternating Ti and Al atoms in the D0(22) superstructure packing.