Turbine systems are provided. A turbine system includes a transition duct comprising an inlet, an outlet, and a duct passage extending between the inlet and the outlet and defining a longitudinal axis, a radial axis, and a tangential axis. The outlet of the transition duct is offset from the inlet along the longitudinal axis and the tangential axis. The duct passage includes an upstream portion and a downstream portion. The upstream portion extends from the inlet between an inlet end and an aft end. The downstream portion extends from the outlet between an outlet end and a head end. The turbine system further includes a joint coupling the aft end of the upstream portion and the head end of the downstream portion together. The joint is configured to allow movement of the upstream portion and the downstream portion relative to each other about or along at least one axis.