Since he had knowingly used his Death Note to extend a human life (a violation of Shinigami law), he was reduced to ash, leaving only his Death Note. Touched by this act, Rem delivered Gelus's Death Note to Misa, since it was her life that he saved.
As a result of knowingly using his Death Note to prolong human existence (a breach of Shinigami regulations), he was annihilated, leaving behind only his Death Note. Moved by this act, Rem handed over Gelus's Death Note to Misa, as it was her life that he had preserved.