He composed the winner entry of Eurovision Song Contest 1989, Rock me, along Stevo Cvikić. They also composed the two previous Yugoslavian entries, Ja sam za ples (sung by Novi Fosili) and Mangup (sung by Srebrna Krila).
He married his wife, Snežana, on December 2, 1990.
- Simonida Milojković. "Rajko Dujmić: Samo mi je vera pomogla da pobedim rak". Blic, 27 November 2011.
- "Rajko Dujmić".
- "Rajko i Snežana Dujmić: 'Naša ljubav je ipak prejaka!'". svet, 23 November 2009.
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