A fitting for a sliding door (4, 5) comprises a rail (3) having at least one track along which a running part (10, 40) equipped with at least one roller (13) can move; the running part (10, 40) includes a holder (11, 41) made of a sheet metal as well as an adapter (14, 44) on which at least one holding means (20, 28, 52, 53, 55) is provided for securing at least one additional functional part (17, 21, 24, 26, 30, 47, 50, 56) to the adapter (14, 44). This allows the fitting for the sliding door to be flexibly adapted for any intended purpose.