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In this report we present our recent investigation on the co-existence of superconducting and semiconducting properties in InN grown on sapphire (0001) by the use of MBE and MOCVD methods. Magneto-transport measurements were done using InN with a carrier density n. from 4 x 10(17) to 4 x 102 cm 3 in the temperature range from 20 mK to 2 K and under the magnetic field (B) up to 23 T-c As a result, even InN samples with n, as low as 4 x 10(17) cm(-3) showed superconductivity at T-c = 0.12 K. The vortex solid of InN was melted by thermal fluctuation and by the external field, similarly to the observation in layered high T-c superconductors. By the Shubnikov-de Haas oscillation measurements it was found that there were substantial carriers spread in the a-b plane which played an essential role not only for the occurrence of the superconductivity, but also for many other unexpected electronic and optical properties of InN. Based on these results we present a possible mechanism of superconductivity in terms of the interaction between the conduction electrons and the fixed d-electrons of In atoms spread in the a-b plane. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.