This paper demonstrates the application of optical amplifiers (OA's) to fiber-optic delay line signal processing. Both erbium-doped fiber amplifiers (EDFA's) and semiconductor optical amplifiers (SOA's) are applicable. Analytical results are presented for both amplified and un-amplified fiber-optic recirculating delay lines (AFORDL and UFORDL). In the AFORDL an OA is inserted in the fiber loop. It is shown that the active AFORDL structure is capable of realizing all-fiber filters not possible with the passive UFORDL. This result is significant because it shows that OA's can function beyond just the trivial optical loss compensation to provide extra flexibility not available in passive designs. An AFORDL design is presented which has a pole near +1 and a zero at -1 in the Z-plane resulting in useful characteristics in the magnitude and phase responses. The results suggest that extension of the concept to higher order filters has the potential to lead to the realization of more complex optical processors.