renault megane starts, but does not hold revs?

i have a renualt megane dynamique 2004. The engine light and service light have come on permanantly. My car starts but sometimes after maybe a twenty minute journey having slowed down or stopping, the engine turns off and i have problems starting the vehicle again and holding the revolutions, if i rev the engine and pull away it eventually stays working. This has happened a few times this week. I have changed the battery, but was ok for a few days but has started doing same thing again. When I slow down the interior lights come on and the engine fails or starts to falter. Could it be the alternator. No battery lights are coming on in the car, radio and all other lights working ok