A new simple method for computing the attenuation (due to dielectric l
osses) of weakly damped electromagnetic waves in a wide class of wave-
guiding structures is suggested. The wave guiding structures considere
d contain time dispersive dielectric media, and restrictions are set n
either on the type of modes nor on the cross-section geometry. Only on
e of the dielectrics of the structure is supposed to be lossy. The wav
e attenuation coefficient results directly from the slope of the wave
dispersion presented as a dependence of the wave number on the permitt
ivity of this dielectric at fixed wave frequency. The method is demons
trated on structures containing cold isotropic plasmas. For this case
the method was found to be applicable even for some configurations wit
h inhomogeneous plasma filling.