A lucky nonepic spellcaster casting
greater dispel magic might be able to dispel an
epic spell. The game mechanics do not change, and
epic spells do not occupy any privileged position allowing them to resist being dispelled other than their presumably high
caster level. Likewise,
epic spells using the
dispel seed can dispel nonepic spells. Such
epic spells use the same game mechanic: The check to dispel is 1d20 + a specified number (usually dispeller's level), and the DC is 11 + the spellcaster's level.
Antimagic field does not automatically suppress
epic spells as it does standard spells. Instead, each time an
epic spell is subject to an
antimagic field, make a dispel check as a 20th-level caster (1d20 + 20). The
epic spell has a DC of 11 + the
epic spell's spellcaster level. If the suppression check is successful, the
epic spell is suppressed like any other spell. If the dispel check is unsuccessful, the
epic spell functions normally.