In order to investigate the geometry of the interactions which myosin molecules make with actin filaments we have studied thick (0.2--0.5 micrometer) transverse sections of striated muscles in the 1 Me V electron microscope at Imperial College. Sections obtained from fixed relaxed frog sartorius muscle and both fixed relaxed and fixed rigor insect flight muscles, show regular electron opaque features between the thick and thin filament profiles. These are thought to be the overlapping images of the many levels of myosin heads that occur in such sections. From the appearances of these images, together with studies of thin transverse sections, it appears that of the possible interactions which one myosin molecule can make, namely that its two component heads interact with the same thin filament or with two different thin filaments, it is the former interaction (both heads on the same filament) which is predominant. Nevertheless appearances have been seen similar to those expected if an interaction of one molecule with two thin filaments occurs. It is concluded that both single filament and two filament interactions can occur depending on the steric convenience of the available actin subunits, but that the single filament interaction occurs in the majority of cases in the muscle states we have studied. Finally it is shown that the myosin filament profiles seen in thick transverse sections may be a very misleading guide to thick filament structure because of the influence which the myosin crossbridge have on the appearance of the profiles.