The critical lines of the binary fluid system may, under certain circumstances, exhibit closed loops in the critical lines. We give some of the necessary requirements for this phenomenon. A distinction is made between free critical loops, as described by type VI in the Scott and van Konynenburg classification, and ''rooted'' critical loops, as found in the shield region. We define rooted loops as closed critical lines that are attached to the critical line structure by means of an unstable critical Line. A general theory is given for the first type and the second type is illustrated with the results obtained from the lattice gas model. It is shown how the appearance of a stable branch detached from the rest of the critical line structure in density space, gives rise to a segment in pressure temperature space. Finally, we show how the position of these rooted critical loops can be found by algebraic means.