The dynamic behaviour of the plasma parameters, including the local electron density, electron temperature, plasma potential and their radial gradients, is studied experimentally during the transitions between low and high confinement modes (L-H transitions) in the H-1 heliac. In particular, a dynamic phenomenon occurring near the threshold conditions for the L-H transition and manifesting itself as a quasi-periodic low-frequency modulation of the local and average plasma parameters is described and discussed. A simple qualitative model for this phenomenon, referred to as L-H cycles, is suggested.