A transition duct support system for a transition duct that channels hot gases from a combustor exit to a gas turbine inlet of a turbine engine, comprising: a transition duct body formed from an outer wall that forms an internal passage extending between an inlet and an outlet of the transition duct body; wherein the transition duct body includes an outlet transition section at the outlet, at least a portion (38, 40, 42) of the outlet transition section being positioned at an oblique angle (48, 52, 54) relative to the outer wall of the transition duct body upstream of the outlet transition section; a transition support frame formed from a body positioned around the transition duct body at the outlet transition section, the transition support frame being of similar shape to the outlet transition section, the transition support frame comprising a radially outer frame wall, opposed frame side walls (58, 60) that extend radially inward from the radially outer frame wall, and a radially inner frame wall that extends between the radially inner ends of the frame side walls (58, 60); and wherein the walls (56, 58, 60, 62) of the transition support frame include at least one inner surface (18, 24) aligned with and positioned proximate to said portion (38, 40, 42) of the outlet transition section, wherein said portion (38, 40, 42) of the outlet transition section comprises a first wall positioned at a first oblique angle relative to the outer wall upstream of the outlet transition section and a second wall positioned at a second oblique angle relative to the outer wall upstream of the outlet transition section, wherein the at least one inner surface (18, 24) of the walls (56, 58, 60, 62) of the transition support frame comprises a first inner surface aligned with and positioned proximate to the first wall of the transition duct body to limit movement in a first direction and a second inner surface aligned with and positioned proximate to the second wall of the transition duct body to limit movement in a second direction that is generally opposite to the first direction, wherein the first wall of the outlet transition section of the transition duct body is positioned at an oblique angle extending generally away from a longitudinal axis of a flow path of the transition duct body and the second wall of the outlet transition section of the transition duct body is positioned at an oblique angle extending generally toward the longitudinal axis of the flow path of the transition duct body. a transition duct body formed from an outer wall that forms an internal passage extending between an inlet and an outlet of the transition duct body; wherein the transition duct body includes an outlet transition section at the outlet, at least a portion (38, 40, 42) of the outlet transition section being positioned at an oblique angle (48, 52, 54) relative to the outer wall of the transition duct body upstream of the outlet transition section; a transition support frame formed from a body positioned around the transition duct body at the outlet transition section, the transition support frame being of similar shape to the outlet transition section, the transition support frame comprising a radially outer frame wall, opposed frame side walls (58, 60) that extend radially inward from the radially outer frame wall, and a radially inner frame wall that extends between the radially inner ends of the frame side walls (58, 60); and wherein the walls (56, 58, 60, 62) of the transition support frame include at least one inner surface (18, 24) aligned with and positioned proximate to said portion (38, 40, 42) of the outlet transition section, wherein said portion (38, 40, 42) of the outlet transition section comprises a first wall positioned at a first oblique angle relative to the outer wall upstream of the outlet transition section and a second wall positioned at a second oblique angle relative to the outer wall upstream of the outlet transition section, wherein the at least one inner surface (18, 24) of the walls (56, 58, 60, 62) of the transition support frame comprises a first inner surface aligned with and positioned proximate to the first wall of the transition duct body to limit movement in a first direction and a second inner surface aligned with and positioned proximate to the second wall of the transition duct body to limit movement in a second direction that is generally opposite to the first direction, wherein the first wall of the outlet transition section of the transition duct body is positioned at an oblique angle extending generally away from a longitudinal axis of a flow path of the transition duct body and the second wall of the outlet transition section of the transition duct body is positioned at an oblique angle extending generally toward the longitudinal axis of the flow path of the transition duct body.