ABSTRACT
We look at ambiguous cycles of ideals in arbitrary quadratic orders. There is much in the literature which deals with this issue, but some of it is confusing or simply incorrect. We will cite these instances, clarify or correct them, and give a complete overview from the point of view of continued fractions and ideal theory. We begin with the real case where we introduce a tool for classifying those ambiguous cycles of ideals which have no ambiguous ideals in them.
