Spiroplasma melliferum BC3 are wall-less bacteria with internal cytoskeletons. Spiroplasma, Mycoplasma and Acholeplasma belong to the Mollicutes, which represent the smallest, simplest and minimal free-living and self-replicating forms of life. The Mollicutes are motile and chemotactic. Spiroplasma cells are, in addition, helical in shape. Based on data merging, obtained by video dark-field light microscopy of live, swimming helical Spiroplasma cells and by cryoelectron microscopy, unravelling the subcellular structure and molecular organization of the cytoskeleton, we propose a functional model in which the cytoskeleton also acts as a bacterial linear motor enabling and controlling both dynamic helicity and swimming. The cytoskeleton is a flat, monolayered ribbon constructed from seven contractile fibrils (generators) capable of changing their length differentially in a co-ordinated manner. The individual, flat, paired fibrils can be viewed as chains of tetramers approximately 100 A in diameter composed of 59 kDa monomers. The cytoskeletal ribbon is attached to the inner surface of the cell membrane (but is not an integral part of it) and follows the shortest helical line on the coiled cellular tube. We show that Spiroplasma cells can be regarded, at least in some states, as near-perfect dynamic helical tubes. Thus, the analysis of experimental data is reduced to a geometrical problem. The proposed model is based on simple structural elements and functional assumptions: rigid circular rings are threaded on a flexible, helical centreline. The rings maintain their circularity and normality to the centreline at all helical states. An array of peripheral, equidistant axial lines forms a regular cylindrical grid (membrane), by crossing the lines bounding the rings. The axial and peripheral spacing correspond to the tetramer diameter and fibril width (100 A) respectively. Based on electron microscopy data, we assign seven of the axial grid lines in the model to function as contractile generators. The generators are clustered along the shortest helical paths on the cellular coil. In the model, the shortest generator coincides with the shortest helical line. The rest, progressively longer, six generators follow to the right or to the left of the shortest generator in order to generate the maximal range of lengths. A rubbery membrane is stretched over (or represented by) the three-dimensional grid to form a continuous tube. Co-ordinated, differential length changes of the generators induce the membranal cylinder to coil and uncoil reversibly. The switch of helical sense requires equalization of the generators' length, forming a straight cylindrical tube with straight generators. The helical parameters of the cell population, obtained by light microscopy, constitute several subpopulations related, most probably, to cell size and age. The range of molecular dimensions in the active cytoskeleton inferred from light microscopy and modelling agrees with data obtained by direct measurements of subunit images on electron micrographs, scanning transmission electron microscopy (STEM) and diffraction analysis of isolated ribbons. Swimming motility and chemotactic responses are carried out by one or a combination of the following: (i). reciprocating helical extension and compression ('breathing'); (ii). propagation of a deformation (kink) along the helical path; (iii). propagation of a reversal of the helical sense along the cell body; and (iv). irregular flexing and twitching, which is functionally equivalent to standard bacterial tumbling. Here, we analyse in detail only the first case (from which all the rest are derived), including switching of the helical sense.