  The majority of the well-studied Delta Scuti stars show frequency pairs in
the power spectra with frequency separations less than 0.06 c/d(0.7 microHz) as
well as amplitude variability. We examine the interpretation in terms of
separate excited stellar pulsation modes,single modes with variable amplitudes,
and observational problems. The variable-phase technique, which examines the
phase jumps near the times of minimum amplitude of an assumed single frequency,
is applied to the extensive data of the star BI CMi, which shows some of the
most extreme behavior. The following results are found for the 5 features in
the power spectrum which could be explained as single modes with variable
amplitudes or as double modes: for three features it can be shown that these
are indeed pairs of separate pulsation modes beating with each other: at times
of minimum amplitude the phase jumps are observed and both the observed
amplitude and phase variations can be predicted correctly by assuming two
separate modes of nearly equal frequencies. Artifacts caused by observational
error,insufficient frequency resolution or variable amplitudes can be ruled
out. A fourth pair has a probable origin in two excited modes, while a 5th case
is inconclusive due to long time scales of variability and small amplitudes.The
existence of close frequencies need to be taken into account in planning the
lengths of earth-based as well as space campaigns so that sufficient frequency
resolution is obtained. Possible reasons for the existence of close frequencies
in Delta Scuti stars are considered.They include the dense frequency spacing
caused by the presence of mixed modes, rotational splitting as well as
near-coincidence of the frequencies of modes with different l values (the
so-called Small Spacing).
