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Topological insulators (TI) constitute a new class of materials that are characterized by the presence of stable (topologically protected) edge surface states of electrons. TI, as well as semiconductor materials can be used for manufacturing photoconductive antennas for generation and detection of terahertz radiation. Therefore, study of the dynamics of hot electrons is very important for understanding the basic mechanisms of carrier relaxation. TI films were grown by MOCVD method: p-type Bi2Te3, n-type Bi2Se3, and Bi1.4Sb0.6Te1.5Se1.5 (BSTS) near the Ren’s curve on the structure-composition diagram. We study the optically induced carrier dynamics with pump energies above a bulk bandgap, and well as the terahertz-induced carrier dynamics with photons energies below the bandgap. It is shown for Bi2Te3 and Bi2Se3 that bulk states contribute to the slow relaxation dynamics, while for bulk insulator BSTS terahertz-induced dynamics is mostly driven through Dirac states on the surface with much higher relaxation rates.