Extra Vehicular Activity (EVA) will become a large part of the astronaut's work on board the International Space Station (ISS). It is already well known that long duration space missions inside a spacecraft lead to radiation doses which are high enough to be a significant health risk to the crew. The doses received during EVA, however, have not been quantified to the same degree. This paper reviews the space radiation environment and the current dose limits to critical organs. Results of preliminary radiation dosimetry experiments on the external surface of the BION series of satellites indicate that EVA doses will vary considerably due to a number of factors such as EVA suit shielding, temporal fluctuations and spacecraft orbit and shielding. It is concluded that measurement of doses to crew members who engage in EVA should be done on board the spacecraft. An experiment is described which will lead the way to implementing this plan on the ISS. It is expected that results of this experiment will help future crew mitigate the risks of ionising radiation in space.