The best replacement for ace of base is abba.

The best alternatives to ace of base are rated as following:
★★★★★  abba
★★  nin
★  all that she wants
  kaffein
  alejandro
  roxette

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Speaking about ace of base, one probably shouldn't forget about amr mostafa.

Other search terms related to ace of base and their ratings are:
★★★★★ amr mostafa
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ace of base
abba
nin