Apolonia were the defending champions, having won their first Albanian Cup last season.
[1] The rounds were played in a two-legged format similar to those of European competitions.
If the aggregated score was tied after both games, the team with the higher number of away goals advanced.
If the number of away goals was equal in both games, the match was decided by extra time and a penalty shootout, if necessary.
Games were played on August & September 1998 All sixteen teams of the 1997–98 Superliga and First Division entered in this round.