Large-amplitude relativistic nonlinear Langmuir waves are analysed using the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two- fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ratio of ion mass to electron mass. The constant energy depends on the ratio of electron velocity to that of light. In the non-relativistic limit large-amplitude relativistic Langmuir waves do not exist. This investigation predicts new findings of large-amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important.