  We present the analysis of the top-quality photometry of RR Lyrae stars in
the globular cluster NGC 6362, gathered over 11 observing seasons by the CASE
project. 16 stars are fundamental mode pulsators (RRab stars) and 16 are first
overtone pulsators (RRc stars). In two stars, previously identified as RRab, V3
and V34, we detect additional periodicity identified as radial first overtone
mode. Lower than usual period ratios (0.730 and 0.728), dominant pulsation in
the radial fundamental mode and presence of a long-period modulation indicate,
that these two variables are not classical RRd stars, but are new members of
the recently identified class of anomalous RRd variables. In a significant
fraction of RRc stars, 63 per cent, we detect additional shorter-period
variability in the (0.60, 0.65)$P_1$ range. This form of double-periodic
pulsation must be common in first overtone RR Lyr stars, as space observations
indicate. The incidence rate we find in NGC 6362, is the highest in
ground-based observations reported so far. We study the properties of these
stars in detail; in particular we confirm that in the colour-magnitude diagram,
this group is adjacent to the interface between RRab and RRc stars, as first
reported in the analysis of M3 observations by Jurcsik et al. The incidence
rate of the Blazhko effect is also very high: we observe it in 69 per cent of
RRab stars and in 19 per cent of RRc stars. Rare, double-periodic modulation is
reported in one RRab and in one RRc star. Finally we discuss V37 - a peculiar
variable in which we detect two close high-amplitude periodicities and
modulation. Its previous classification as RRc must be treated as tentative.
