A theoretical model interpreting propagating disturbances of EUV emission i
ntensity, recently observed in coronal loops, is constructed in terms of sl
ow magnetoacoustic waves. The model is one-dimensional and incorporates eff
ects of nonlinearity, dissipation due to finite viscosity and thermal condu
ction, and gravitational stratification of plasma in the loop. It has been
found that, for the observationally detected parameters of the waves, the m
ain factors influencing the wave evolution are dissipation and stratificati
on. The upwardly propagating waves of observed periods (5-20 min) are found
to decay significantly in the vicinity of the loop apex, explaining the ra
rity of observational detection of downwardly propagating waves. The model
provides a theoretical basis for development of MHD seismology of the coron
al loops.