It is known that the bound mode on many printed-circuit transmission lines becomes leaky above some critical frequency and that the leakage occurs in the form of a surface wave on the surrounding substrate. At still higher frequencies the leakage can occur into more than one surface wave. Depending on the structure and the geometric parameters, the physical phenomena can take on different forms. This paper first describes the various forms that we have found in our study and then focuses on the one that involves an unusually wide spectral gap at the onset of the additional surface wave. The wide-spectral-gap case is examined in more detail because its features differ in important ways from those of the usual spectral gap. Theoretical calculations and measured results are presented which describe these new features.