  Coronal waves are an important aspect of the dynamics of the plasma in the
corona. Wavefront dislocations are topological features of most waves in nature
and also of magnetohydrodynamic waves. Are there dislocations in coronal waves?
The finding and explanation of dislocations may shed light on the nature and
characteristics of the propagating waves, their interaction in the corona and
in general on the plasma dynamics. We positively identify dislocations in
coronal waves observed by the Coronal Multi-channel Polarimeter (CoMP) as
singularities in the Doppler shifts of emission coronal lines. We study the
possible singularities that can be expected in coronal waves and try to
reproduce the observed dislocations in terms of localization and frequency of
appearance. The observed dislocations can only be explained by the interference
of a kink and a sausage wave modes propagating with different frequencies along
the coronal magnetic field. In the plane transverse to the propagation, the
cross-section of the oscillating plasma must be smaller than the spatial
resolution, and the two waves result in net longitudinal and transverse
velocity components that are mixed through projection onto the line of sight.
Alfv\'en waves can be responsible of the kink mode, but a magnetoacoustic
sausage mode is necessary in all cases. Higher (flute) modes are excluded. The
kink mode has a pressure amplitude that is smaller than the pressure amplitude
of the sausage mode, though its observed velocity is larger. This concentrates
dislocations on the top of the loop. To explain dislocations, any model of
coronal waves must include the simultaneous propagation and interference of
kink and sausage wave modes of comparable but different frequencies, with a
sausage wave amplitude much smaller than the kink one.
