  Context. The analysis of stellar oscillations is one of the most reliable
ways to probe stellar interiors. Recent space missions such as Kepler have
provided us with an opportunity to study these oscillations with unprecedented
detail. For many multi-periodic pulsators such as {\gamma} Doradus stars, this
led to the detection of dozens to hundreds of oscillation frequencies that
could not be found from ground-based observations. Aims. We aim to detect
non-uniform period spacings in the Fourier spectra of a sample of {\gamma}
Doradus stars observed by Kepler. Such detection is complicated by both the
large number of significant frequencies in the space photometry and by
overlapping non-equidistant rotationally split multiplets. Methods. Guided by
theoretical properties of gravity-mode oscillation of {\gamma} Doradus stars,
we developed a period-spacing detection method and applied it to Kepler
observations of a few stars, after having tested the performance from
simulations. Results. The application of the technique resulted in the clear
detection of non-uniform period spacing series for three out of the five
treated Kepler targets. Disadvantages of the technique are also discussed, and
include the disability to distinguish between different values of the spherical
degree and azimuthal order of the oscillation modes without additional
theoretical modelling. Conclusions. Despite the shortcomings, the method is
shown to allow solid detections of period spacings for {\gamma} Doradus stars,
which will allow future asteroseismic analyses of these stars.
