  The nature of the observed amplitude variability of several modes in the
Delta Scuti star FG Vir is examined. In this star, three frequencies show
strong amplitude and phase variations. In the power spectrum, these frequencies
also show up as frequency doublets. However, since true amplitude variability
of a single frequency can also lead to (false) frequency doublets in the power
spectrum, a specific test examining in detail the observed amplitude and phase
variations of an assumed single frequency is applied. For the frequencies at
12.15 and 23.40 cycle/day it is shown that amplitude variability of a single
mode can be ruled out. In particular, an important property of beating between
two modes is fulfilled: the amplitude and phase vary synchronously with a phase
shift close to 90 degrees. The origin of the amplitude variability of a third
mode, viz. near 19.86 c/d, is not clear due to the long beat period of 20+
years, for which the amplitude/phase test suffers from gaps in the coverage.
However, even for this frequency the amplitude variations can be expressed well
by a mathematical two-mode model.
  If we examine these three close frequency pairs together with other (usually
more widely separated) close frequencies in FG Vir, 18 pairs of frequencies
with separations closer than 0.10 c/d have been detected. It is shown that the
majority of the pairs occur near the theoretically expected frequencies of
radial modes. Mode identifications are available for only a few modes: the only
detected radial mode at 12.15 c/d is part of a close pair.
  It is shown that accidental agreements between the frequencies of excited
modes can be ruled out because of the large number of detected close frequency
doublets.
