At the time this study was undertaken, linear electric machines (LEMs) were relatively new. Compared with rotating machines, relatively little work had been done on them. Although LEMs are finding ready applications, they concern the polyphase LEMs only. In some applications, they concern the polyphase LEMs only. In some applications LEMs have advantages over rotating machines because of an absence of gears or rotary-to-linear converters, a high reliability and the possibility of very high speed of the travelling field. However, problems arise from the undesired characteristics of big air gaps, lossy end-effects, low efficiency, and a low power factor. This thesis is concerned with a device called a single phase travelling wave linear induction motor (STLIM). Unlike most electrical machines, STLIMs utilise propagating magnetic waves, waves that are obtained by arranging the windings of the linear primary coils and shunt capacitors to simulate a transmission line. The waves drive linear conducting sheet secondaries. The STLIMs have some interesting characteristics: (1) most importantly, the speed of STLIM can be varied by the value of shunt capacitance or series coil inductance; (2) due to the attenuated travelling wave nature, the exit end-effect is self-reduced; (3) the device operates at nearly unity power factor for all ranges of slip; (4) it is a constant current device. Although the experimental efficiency demonstrated in the present work has not been high, it is still compatible with either small single phase induction motors or polyphase linear induction motors of the same physical dimensions. Original mathematical theories of STLIMs have been presented that have been based on one-dimensional current sheet analysis and adapted transmission line distributed parameter theory. The developed experimental models and the tests that have been carried out substantiate the theories.