The CH2CF2- and CF2CF2- anions were studied by using theoretical (DFT) B3LYP, MP2, and QCISD methods in conjunction with large basis sets. The standard split valence plus polarization basis sets augmented with diffuse functions on heavy atoms (Bn+) are considered to be appropriate for these anions. Structures (anti, syn, planar, and perpendicular) of the two anions were studied based on B3LYP geometry optimization, frequency analysis, and intrinsic reaction coordinate (IRC) calculations. For CF2CF-, a new minimum-energy structure having C-2 symmetry was found in the IRC calculations. Anti structure is the most stable for each of the two anions. Syn structure of CF2CF2- is the transition state for the C2 reversible arrow C2 interconverting process, and syn structure of CH2CF2- does not exist. The planar structures of the two anions are the transition states for the anti reversible arrow anti interconverting processes. The isotropic hyperfine coupling constants (hfcc's) in anti-CH2CF2- and anti-CF2CF2- were explicitly calculated using the B3LYP and MP2(full) methods, and the calculations with the 6-311+G(2d,p) basis set predict hfcc values in good agreement with experiment. Adiabatic and vertical electron affinity (AEA and VEA) values of the CH2CF2 and CF2CF2 molecules were calculated using the B3LYP and QCISD methods. The QCISD/6-311+G(2d,p) calculations for the two molecules predict the values of the VEAs associated with the pi* states (B-2(1) and B-2(2g), respectively) of the anions in quite good agreement with the experimental VEA(pi*) values. It is argued that the sigma* states of the two anions are the ground states at the molecular geometries and that the existence of the anti structures of the two anions is considered as a consequence of the pseudo-Jahn-Teller effect.