  This paper summarises two recently developed techniques in power spectral
analysis and their application to a sample of X-ray light curves of accreting
collapsed objects in active galactic nuclei and X-ray binaries. The first
technique is designed to carry out detailed model fitting of continuum power
spectrum components arising from noise variability by using maximum likelihood
methods. The technique is applied to the light curves of a number of highly
variable AGNs observed with EXOSAT. Substantially steeper logarithmic power
spectrum slopes are obtained than previously estimated with standard methods.
The second technique was devised in order to reveal coherent periodicities in
the presence of ``coloured" (i.e. non--white) noise variability components from
the source. To this aim the power spectra are searched for significant narrow
peaks superposed on the ``coloured" continuum components. We present the
results of a search for an orbital modulation in the light curves of a sample
of 25 low mass X--ray binaries (LMXRBs), for which the orbital period is either
unknown or detected only at optical wavelengths. This led to the discovery of a
significant X--ray orbital modulation at the few percent level in the burster
MXB1636-539.
