Data on an prolonged period of EUV emission after a sudden rise in bri
ghtness recorded by the Extreme Ultra-violet Explorer (EUVE) for the s
tar AU Mic are discussed. Intense emission was observed for roughly 12
hours after each of two impulses, which exceeds by 10 times the radia
tion cooling time of coronal loops with typical flare plasma densities
. Difficulties are pointed out for two explanations for this phenomena
suggested earlier: emission by dense loops in the main phase of the f
lare, and emission of rarified plasma in coronal transients. Joint ana
lysis of observations of the 65 - 190 Angstrom band and the 93.9 Angst
rom FeXVIII line showed a temporary change in the emission measure of
the source. The total energy emitted during approximately 12 hours was
3 x 10(35) erg. The concept of post-eruptive energy release is used t
o explain the prolonged emission in the EUV. The source of the emissio
n is a system of high coronal loops with size exceeding the radius of
the star. Such loop systems of already-cooled plasma have been observe
d on the Sun in H-alpha during powerful flares (for example, June 15,
1991) after the transient has gone. Some additional energy input into
the loop system from vertical current layers is possible, which prolon
gs the emission. The proposed phenomenon is a new type of surface acti
vity on late stars, which is intermediate between impulsive flares on
red dwarves and prolonged and powerful events on the subgiant componen
ts of RS CVn double systems.