In each of the three families of molecular motors - myosins, kinesins and dyneins - it is possible to extract motors from their native environment, prepare assemblies of them on a plane surface and use them to transport their respective associated fibres, either actin filaments (the myosins) or microtubules, in an aqueous environment. For these motors to be useful in nanofabrication, it is essential that external control can be applied to the following properties: (a) translocation speed; (b) translocation direction; (c) activation and arrest. These characteristics can be controlled by altering the chemical and/or the physical environment of the motors. For dynein, experiments show that the translocation speed depends on the concentration of ATP and is acutely sensitive to the proportion of motors phosphorylated within the assembly. The direction of motion can be determined by distributing the motors on highly oriented polymer films and making use of the polarisation characteristics of the transported fibres. Switching the motors on and off could, in principle, be achieved by rapid addition or removal of ATP, for example by making use of caged compounds. To better understand how these natural molecular systems operate, so that appropriate experimental procedures can be formulated to investigate and take advantage of the properties of biological motors in the design and construction of nanomachines, we have modelled the translocation process theoretically and by computer simulation. In the experimental situation, the fibre moves linearly along its own axis with little deviation and, generally, no reversal. Accordingly, our initial analyses are of a system consisting of a linear array of motors, randomly arranged and propelling a fibre. Each motor undergoes a cycle, during which, in the so-called duty phase, it forms a transient, strong attachment to the fibre and moves it linearly. We have made theoretical and computer-based predictions of the velocity of microtubule translocation as a function of microtubule length for situations where all the motors are identical and activated randomly both with respect to time and position in the array. Within the model system, parameters that could be varied include the cycle time, the proportion of the cycle occupied by the duty phase and the step size, i.e. the maximum distance a motor can move a fibre in one cycle. The predictions of theoretical analysis and computer simulation are the same, and indicate that the velocity rises to a plateau as the microtubule length increases in a manner similar to that observed experimentally. For dynein, the experimental results are correctly predicted if it is assumed that the duty phase occupies a small fraction (<10%) of the total motor cycle. The results of experiments where a small proportion of the dynein motors are phosphorylated to operate at a faster rate than untreated motors are also correctly predicted by the analyses. The agreement between the analytical and computational approaches validates the computer simulation program, which we are currently using to investigate situations intractable by theoretical analysis and so provide information of value to molecular nanotechnology.