Terahertz (THz) transmission, photoresistance, and electrical conductivity experiments were carried out at 4.2 K on a sample with modulation-doped CdTe/Cd _1-xMg _xTe multiple quantum wells. The measurements were carried out as a function of a magnetic field B up to 9 T and a radiation frequency between 0.1 and 0.66 THz. A broad minimum in the transmission curve was observed at magnetic fields corresponding to the cyclotron resonance at given THz frequency which was followed at larger fields by an oscillatory signal, periodic in B ⁻¹. Shubnikov-de Haas oscillations were observed in magnetoconductivity and in photoresistance. Each of these experimental signals revealed the same electron concentration equal to (1.01 ± 0.03) ∙1012 cm ⁻². THz spectroscopy results are compared with data obtained on a single quantum well and are discussed from the point of view of using such multiple quantum wells as THz optical elements.