The transition from a stable orthorhombic structure to a hexagonal structure has been revealed in Tb1−xYxMnO3 multiferroics at x = 0.2–0.4. It has been shown that almost single-phase crystals with an orthorhombic or hexagonal structure can be obtained by choosing the growth conditions. It has been found that the magnetic and dielectric properties of orthorhombic single crystals with x = 0.2–0.3 are similar to the properties of pure TbMnO3 and are characterized by a strong anisotropy of the magnetic susceptibility at low temperatures and by the presence of a number of magnetic phase transitions, including those to the ferroelectric state. New spontaneous (T ≤ 15 K) and magnetic-field induced (H | C6) phase transitions accompanied by the appearance of an uncompensated rare-earth magnetic moment ∼1 μB/mole have been observed in hexagonal single crystals with x = 0.3–0.5.