The dielectric response of strontium barium niobate with 61% Sr has been studied from kHz to THz frequencies by means of several techniques (IR and time domain THz spectroscopy, the coaxial technique and dielectric spectroscopy) over a wide temperature interval: 20–600 K. A strong dielectric anisotropy is present in all the results. Relaxor ferroelectric properties were detected in εc*(T,ν). At very high temperatures a strong relaxation appears in the microwave and THz range, which shifts and broadens to lower frequencies on cooling and then splits into two components. The high frequency one is seen in the THz range at high temperatures and the strong low frequency one weakens below the temperature Tm of the smeared permittivity maximum and broadens extremely in the spectra leaving a constant-loss background at very low temperatures. This relaxation is responsible for the dielectric anomaly near the ferroelectric transition. No anomalies in phonon frequencies were observed, which gives evidence relating to the order–disorder mechanism of the phase transition. The response perpendicular to the polar axis shows anomalous features at low temperatures, which could be connected with the shift of the low frequency limit of a broad dispersion (much weaker than along the polar axis) from the GHz range at 200 K to the kHz range at 40 K. There is no clear evidence of a new phase transition below 100 K suggested by some authors.