A valve opening duration control apparatus comprising: a camshaft ; a cam unit on which a cam is formed, wherein the camshaft is inserted into the cam unit ; a first guide bracket and a second guide bracket into which the camshaft is inserted; a wheel housing movably mounted to the first guide bracket and the second guide bracket , respectively; an internal wheel mounted on the camshaft and rotatably mounted on each wheel housing of the first guide bracket and the second guide bracket , wherein the internal wheel is configured of transmitting a rotation of the camshaft to the cam unit ; a worm wheel mounted on the first guide bracket and the second guide bracket , respectively to engage with each wheel housing ; a control shaft which is rotatably mounted on the first guide bracket and the second guide bracket , and engages with each worm wheel to move a position of the wheel housing according to rotation thereof; a connecting member that connects the first guide bracket and the second guide bracket ; an upper guide boss formed on the first guide bracket and the second guide bracket , respectively; a guide shaft formed at the wheel housing , wherein the guide shaft is movably inserted into the upper guide boss and formed with a guide thread ; an internal thread formed on an inside of the worm wheel and engaged with the guide thread , and an external thread formed on an outside of the worm wheel ; and a control worm formed on the control shaft and engaging with the external thread , such that the worm wheel rotates by the rotation of the control shaft and changes the relative position of the wheel housing to the camshaft , such that, when the position of the wheel housing moves upper or lower relative to the rotation center portion of the camshaft , the relative rotation speed of the cams with respect to the rotation speed of the camshaft are changed. a camshaft ; a cam unit on which a cam is formed, wherein the camshaft is inserted into the cam unit ; a first guide bracket and a second guide bracket into which the camshaft is inserted; a wheel housing movably mounted to the first guide bracket and the second guide bracket , respectively; an internal wheel mounted on the camshaft and rotatably mounted on each wheel housing of the first guide bracket and the second guide bracket , wherein the internal wheel is configured of transmitting a rotation of the camshaft to the cam unit ; a worm wheel mounted on the first guide bracket and the second guide bracket , respectively to engage with each wheel housing ; a control shaft which is rotatably mounted on the first guide bracket and the second guide bracket , and engages with each worm wheel to move a position of the wheel housing according to rotation thereof; a connecting member that connects the first guide bracket and the second guide bracket ; an upper guide boss formed on the first guide bracket and the second guide bracket , respectively; a guide shaft formed at the wheel housing , wherein the guide shaft is movably inserted into the upper guide boss and formed with a guide thread ; an internal thread formed on an inside of the worm wheel and engaged with the guide thread , and an external thread formed on an outside of the worm wheel ; and a control worm formed on the control shaft and engaging with the external thread , such that the worm wheel rotates by the rotation of the control shaft and changes the relative position of the wheel housing to the camshaft , such that, when the position of the wheel housing moves upper or lower relative to the rotation center portion of the camshaft , the relative rotation speed of the cams with respect to the rotation speed of the camshaft are changed. <EOS>