Lordi, whose "Hard Rock Hallelujah" won the contest with a record number of points late Saturday in Athens, do not appear publicly without their monster costumes.
In interviews and on their band Web site, they stick to their stage names: Mr. Lordi, Kita, Amen, Awa and Ox.
But several European media appeared determined to blow their cover Monday, publishing what they said were pictures of the group, unmasked.
Britain's Daily Mail and Swedish tabloids Expressen and Aftonbladet all had pictures reportedly showing the band members without monster garb.
Finnish media have previously reported the names of four of the five musicians, but band founder Tomi Putaansuu, or Mr. Lordi, asked that media don't publish pictures without costumes, the AP reports.
In Finland, a perennial Eurovision loser, fans were still ecstatic about the surprise victory.
Tabloids on Monday featured 20-page supplements and posters of Lordi, and the growling monsters' song blared on radios and as background music on TV weather shows.
Newspapers featured pictures of celebrating people jumping nude into fountains; the government promised money to host next year's Eurovision contest; and Rovaniemi, Putaansuu's home town in Lapland, said it will name a square after Lordi. Skeptical journalists apologized publicly for doubting that the group would be successful.
Lordi was scheduled to hold a news conference later Monday, but it was unclear whether the group would appear in their latex monster costumes.
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