Assuming that the number of ionizations events within short segments of DNA-size volumes is a major factor of the biological effectiveness of ionizing radiation, we have designed and manufactured a new nanodosimetric detector counting ionization events in small wall-less gas volumes, which simulate such DNA segments. The detector measures individual ionizations in low-pressure (~1 Torr) propane or any other gas corresponding to a tissue-equivalent cylindrical volume of 2-4 nm diameter and up to 30 nm length. While first nanodosimetric event spectra with protons and alpha particles are being obtained, it is important to develop and test a theory that relates these spectra to biological endpoints such as strand breakage, mutations, and lethal cellular events. This paper describes the two-compartment theory, which is based on the premise that energy deposition in nanometer sites can be broadly divided into two categories: a low-energy deposition compartment comprising events with a total number of 2-5 ionizations, and a high-energy deposition compartment comprising events containing 6-10 ionizations. Under standard biochemical conditions, these events will lead to different biological consequences. The fate of DNA lesions produced by low-energy deposition events will mostly depend on the repair capacity of the irradiated cells, whereas events produced by high-energy deposition events will be irreparable. These events are therefore the biologically most relevant lesions, since they inevitably lead to mutation and cell death.