The undulatory propagation mechanisms of long streamers in a highly no
nuniform electric field are considered, and the interrelations between
main characteristics of the propagation process are clarified. The po
tentialities of the streamer theoretical models are analyzed and the r
esults of their applications are systematized. The necessity of solvin
g a self-consistent problem, involving both the processes at the ioniz
ation-wave front and in the channel behind the front, is shown. One-di
mensional and quasi-two-dimensional streamer simulation models with a
priori assigned constant channel radius are considered; their simulati
on results are found out to depend critically on the channel radius. A
hypothesis postulating the ionization mechanism of streamer channel e
xpansion in the field of its own space-charge field, was developed and
corroborated by computation results. The sensitivity of the computati
on results to the rates of the elementary processes incorporated into
the model was investigated in detail. The models involving detailed ki
netics are shown to be sufficiently stable. This justifies the use of
two-dimensional models of streamers in atmospheric air.