This paper describes theory related to a programme of tests made on titanium and Inconel bolts to detect and measure fatigue cracks in the threads. The Crack Microgauge instrument, which uses the a.c. potential difference method of detection, was used in the experimental investigation. A continuous sequence of probe signals, taken between successive crowns of the thread as the bolt is turned, yields a characteristic pattern of response in which there is a main signal, obtained when the probe spans the crack, accompanied by a sequence of satellite signals, which arise when the probe spans the threads adjacent to the crack. The theory developed in the paper provides the relation between crack depths and probe signals measured and it explains and quantifies the system of satellite signals found on the threads upstream and downstream of the cracked thread. Since the electrical skin depths and the radii of the bolts involved were much larger than the length scales of the crack and the thread, a two-dimensional thick-skin theory for the electromagnetic field is appropriate. Satisfactory agreement between theory and experiment was obtained. The tests were made on threads with artificial notches cut at the thread roots, which have a symmetrical satellite system, and on naturally occurring fatigue cracks, which give rise to asymmetric satellite systems. The theory shows that there is a relation between the asymmetry and the location of the crack on the thread. Only a few complete measurements of satellite asymmetry were recorded in the tests, which were completed before the mathematical theory was developed. The work suggests that in future tests of this type it would be beneficial to have more detailed investigation of the satellite signal asymmetry so that the location of the cracks on the threads can be more closely specified.