Disclosed are a conjugated diolefin (co) polymer rubber formed from either a conjugated diolefin or a conjugated diolefin and an aromatic vinyl compound, wherein the (co) polymer rubber has a primary amino group and an alkoxysilyl group which are bonded to a (co) polymer chain; a process for producing the same; a rubber composition; a composite; and a tire. The (co) polymer rubber has satisfactory processability, and can give an automotive tire tread having a balance among wear resistance, failure characteristics, low hysteresis loss and wet-skid characteristics.