We have attempted to separate the thermal and nonthermal component of the radio emission from the Large Magellanic Cloud (LMC), using either Ha or far infrared data. On a large scale (51′ resolution = 750 pc) the differences arising from the different techniques are rather small. A significant variation of the nonthermal spectral index over the LMC is found. The main clue is a generally steeper nonthermal spectrum in the western part of LMC than in the eastern one (around the 30 Doradus region. This may be due to recent injection of cosmic ray electrons into the interstellar medium by supernovae in this active star forming region, which away from these regions age as they propagate and lose energy.