We consider dense toroidal structures of DNA molecules in cells and viruses. The problem needs special studying. For one thing the space scale of the system being small one has to admit that such structures must be compact enough to accommodate a molecule of the DNA, for another the molecule should be easily accessible for various biochemical processes, for example replication. Theoretical treatment of the problem runs across substantial diculties, and there- fore there is a need for the experimental investigation of the DNA conformation in cells and viruses. The XFEL could be instrumental to that end.