In this paper, we consider the elementary processes involved in the appearance of a simple twin wake in the two-dimensional steady aligned flow of an electrically conducting viscous incompressible fluid in a uniformaly applied magnetic field. Fundamental relations between the twin wake and its elementary process are generally discussed, and the corresponding initial-value problem is formulated. Then, the solution of the initial-value problem corresponding to the above simple twin wake is obtained, and two limiting cases with the magnetic Prandtl number near one and zero (or infinite) are discussed in detail. In both cases, it is found that negative vorticity appears in between the main positive vorticity associated with the two Alfven spots. This fact gives some clue to the understanding of the property of twin wakes. As an application, the crossed-flow case is also discussed, and a conjecture upon the vorticity distribution is made.