We present the results of detailed frequency analyses of a sample of thirteen confirmed slowly pulsating B stars. Our analysis is based on a combination of elaborate photometric and spectroscopic data-sets. The original sample consists of a mixture of five confirmed slowly pulsating B stars and twelve candidate slowly pulsating B stars discovered thanks to the photometric measurements of the HIPPARCOS satellite. HD55522 and HD131120 turn out to be chemically peculiar stars. HD169978 and HD69144 are two ellipsoidal variables for which no intrinsic variability is found. At least nine of the thirteen studied slowly pulsating B stars are multi-periodic. For HD74195, HD85953, HD123515 and HD215573, the observed frequency spacings suggest that we are dealing with frequency multiplets. For the apparent mono-periodic binary HD24587, it is not clear if the observed variations are induced by stellar pulsation and or by rotation modulation. We highlight the statistical character of the observed pulsational properties of our sample.