1975–76 saw John Neal's starlets captained by Eddie May, again shocked the football world by reaching the quarter-finals of the European Cup Winners' Cup after another sparkling cup run and multiple defeats of higher quality opponents. In the first round Wrexham beat Swedish team Djurgårdens IF 3–2 on aggregate. They then managed to knock out Polish side Stal Rzeszow 3–1 on aggregate. Wrexham played Belgian champions Anderlecht in the quarter finals and narrowly lost 2–1 to the eventual winners of the competition.