Uniaxial ferroelectrics with tetragonal tungsten bronze structure are important functional materials with photorefractive, electrooptic, piezoelectric, and pyroelectric properties. SrxBa1−xNb2O6 (SBN100x) with x > 50 is known as a typical uniaxial relaxor ferroelectric, while CaxBa1−xNb2O6 (CBN100x) undergoes nearly normal ferroelectric phase transitions. Single crystals of CSBN100x = [x(CBN28) + (1 − x) (SBN61)] = xCa0.28Ba0.72Nb2O6 + (1 − x) Sr0.61Ba0.39Nb2O6 with nominal x = 0.00, 0.25, 0.50, 0.75, and 1.00 were studied to clarify the dynamical properties at the crossover from relaxor (x = 0) to normal (x = 1) ferroelectric behavior. The longitudinal acoustic (LA) and transverse acoustic (TA) modes and a central peak (CP) related to the relaxation process of polarization fluctuations along the polar c-axis were studied in uniaxial ferroelectric CSBN single crystals as a function of temperature via Brillouin scattering spectroscopy. A CBN28 (x = 1.00) crystal shows the sharp elastic anomaly of the LA mode in the gigahertz range toward Curie temperature, Tc. However, those of CSBN25 (x = 0.25) and SBN61 (x = 0.00) crystals show diffusive anomalies due to stronger random fields. The relaxation time determined from the width of a CP shows a critical slowing down in the vicinity of Tc. The elastic anomaly and slowing down of relaxation time of CSBN100x crystals become diffusive in the vicinity of Tc as the CBN28 content decreases. The origin of the crossover from relaxor to normal ferroelectric phase transitions is discussed in terms of the difference in the A1 and A2 sites’ occupancies.