  This thesis investigates phenomena occurring in black-hole accretion discs
which are likely to induce high-frequency quasi-periodic variability. Two
classes of pseudo-relativistic theoretical models are studied. The first is
based on the stability of transonic accretion flows and its connection to a
disc instability that takes the form of propagating waves (viscous
overstability). The second class of models looks at accretion-disc oscillations
which are trapped due to the non-monotonic variation of the epicyclic frequency
in relativistic flows. In particular, it focuses on inertial waves trapped
below the maximum of the epicyclic frequency which are excited in deformed,
warped or eccentric, discs. The influence of a transonic background on the
propagation of these inertial modes is also investigated.
