In a first report on the results of a multi-site campaign in 2001 of photometric and spectroscopic observations of the active semi-detached Algol-type system RZ Cas, we concentrate on the radial velocity (RV) variations. Using weak absorption lines we obtain an improved orbital solution for both components. In the orbital RV curve we observe a strong, asymmetric rotation effect. For the first time we detect rapid spectroscopic multi-mode pulsations in an Algol system. Whereas the photometrically observed oscillations were dominated by monoperiodic pulsations at frequency 64.19c/d until the year 2000, we find in 2001 a multiperiodic behaviour with two dominant frequencies of f1=56.600c/d and f2=64.189c/d. Both modes show amplitude variations over the orbital phase with a minimum at orbital phases phi=0.6-0.8 and a maximum just after the primary minimum (f2) and at phi=0.25 (f1). The different shape of amplitude modulation of the f1 and f2 modes points to different (l,m) mode structures. The modulation itself can be explained by assuming a variable extinction due to gas streams and an inhomogeneous accretion annulus that weakens the light from different regions of the primary depending on its orbital position.