<p>The present invention relates to an apparatus for producing three-dimensionally curving bent tubes by means of a core member and a tubular die which are disposed off-centrally from each other. More precisely, the apparatus according to the present invention comprises (a) a bending die (21) having an axi-symmetric inner surface for passing a tube member therethrough; (b) a core member (22) having an axi-symmetrical outer surface and disposed in the bending die (21) in a spaced relation to the inner surface of the bending die so that the core member (22) passes through a hollow space defined by the tube member and the tube member passes between the second inner surface and the outer surface of the core member; and (c) positioning means for positioning the bending die (21) relative to the tubular die in a plane pependicular to an axis of the tubular die.</p>