The new types of surface electromagnetic waves (polaritons) in tetrago
nal antiferromagnetics (AFM) with magnetoelectrical (ME) effect are in
vestigated theoretically. The main attention is paid to two cases: whe
n the AFM vector L is parallel and normal both to surface of specimen
and electromagnetic wave vector. In the first case polaritons exist on
ly in the frequency range of optical phonons oscillations. ME effect r
esults in the effect of inambiguity. In the second case at large magni
tude ME effect the surface waves can exist both near to frequencies of
a magnetic subsystem oscillations, and in the region of frequencies o
f optical phonons oscillations. At small ME effect surface waves exist
only near to frequencies range of optical phonons oscillations. In th
is geometry the polaritons oscillate deep into sample with period whic
h is proportional to ME interaction succeptibility magnitude.