Nondissociative electron attachment to c-C7F14 and C6F6 is investigated by measuring the velocity distribution of K+ ions formed via electron transfer in collisions with velocity selected K(np) Rydberg atoms and by measuring the decay of the product negative ions during passage to a detector. Collisions with C7F14 lead to the production of free electrons and of long-lived (tau > 100 mu s) C7F14-* ions. The free electrons, which result from autodetachment, are all created within a very short time period (tau less than or similar to 15 ps) following initial electron capture. Collisions with C6F6 result in the formation of C6F6-* ions that have a broad range of lifetimes against autodetachment. A possible reaction model involving competition between autodetachment and intramolecular vibrational relaxation is discussed.