A combustion turbine subsystem comprising: a first stage blade array having a plurality of blades extending in a radial direction from a rotor assembly for rotation in a circumferential direction, said circumferential direction having a tangential direction component, the rotor assembly axis defining a longitudinal direction; a plurality of combustors located longitudinally upstream of the first stage blade array and located radially outboard of the first stage blade array; and a plurality of transition duct bodies, each having an internal passage extending between an inlet and an outlet, wherein the outlet of each transition duct body is radially aligned with the inlet of an adjacent transition duct body, each transition duct body extending between a respective combustor and the first stage blade array to receive the gas flow exhausted by the combustor into its internal passage via its inlet, the outlets of the transition duct bodies discharging the gas flows from their internal passages onto the first stage blade array, wherein the outlet of each transition duct body is offset from its inlet in the longitudinal direction, the radial direction and the tangential direction and the internal passage of the transition duct body is curved to the offset outlet, whereby the gas flow discharged from the outlet of each transition duct body is at an angle between the longitudinal direction and the tangential direction, wherein the width of each internal passage in the tangential direction decreases from its inlet toward its outlet, wherein the gas flow discharged by each outlet discharges substantially in a plane defined by the longitudinal direction and the tangential direction, whereby the discharged gas flow direction has substantially no radial component, wherein the direction of the gas flow discharged by the outlet of each internal passage has substantially no radial component due to a decrease or complete discontinuance of radially inward curvature along the radially outer top and radially inner bottom of the internal passage before approaching its outlet. a first stage blade array having a plurality of blades extending in a radial direction from a rotor assembly for rotation in a circumferential direction, said circumferential direction having a tangential direction component, the rotor assembly axis defining a longitudinal direction; a plurality of combustors located longitudinally upstream of the first stage blade array and located radially outboard of the first stage blade array; and a plurality of transition duct bodies, each having an internal passage extending between an inlet and an outlet, wherein the outlet of each transition duct body is radially aligned with the inlet of an adjacent transition duct body, each transition duct body extending between a respective combustor and the first stage blade array to receive the gas flow exhausted by the combustor into its internal passage via its inlet, the outlets of the transition duct bodies discharging the gas flows from their internal passages onto the first stage blade array, wherein the outlet of each transition duct body is offset from its inlet in the longitudinal direction, the radial direction and the tangential direction and the internal passage of the transition duct body is curved to the offset outlet, whereby the gas flow discharged from the outlet of each transition duct body is at an angle between the longitudinal direction and the tangential direction, wherein the width of each internal passage in the tangential direction decreases from its inlet toward its outlet, wherein the gas flow discharged by each outlet discharges substantially in a plane defined by the longitudinal direction and the tangential direction, whereby the discharged gas flow direction has substantially no radial component, wherein the direction of the gas flow discharged by the outlet of each internal passage has substantially no radial component due to a decrease or complete discontinuance of radially inward curvature along the radially outer top and radially inner bottom of the internal passage before approaching its outlet.