The manipulation of single magnetic molecules may enable new strategies for high-density information storage and quantum-state control. However, progress in these areas depends on developing techniques for addressing individual molecules and controlling their spin. Here, we report success in making electrical contact to individual magnetic N@C(60) molecules and measuring spin excitations in their electron tunnelling spectra. We verify that the molecules remain magnetic by observing a transition as a function of magnetic field that changes the spin quantum number and also the existence of non-equilibrium tunnelling originating from low-energy excited states. From the tunnelling spectra, we identify the charge and spin states of the molecule. The measured spectra can be reproduced theoretically by accounting for the exchange interaction between the nitrogen spin and electron(s) on the C(60) cage.