In this paper, we present an efficient neural network for end-to-end general purpose audio source separation. Specifically, the backbone structure of this convolutional network is the SUccessive DOwnsampling and Resampling of Multi-Resolution Features (SuDoRMRF) as well as their aggregation which is performed through simple one-dimensional convolutions. In this way, we are able to obtain high quality audio source separation with limited number of floating point operations, memory requirements, number of parameters and latency. Our experiments on both speech and environmental sound separation datasets show that SuDoRMRF performs comparably and even surpasses various state-of-the-art approaches with significantly higher computational resource requirements.