Positive-negative asymmetry in thought can involve both cognitive asymmetry, (thinking about characteristics that a stimulus has versus does not have), which we predict will be large and preponderantly a positivity bias, and affective asymmetry (thinking about desirable versus undesirable characteristics that the stimulus has or has not), predicted to be small and to fluctuate predictably in direction. The first four of the 10 studies reported here investigate asymmetries in thinking ability, measured by giving people directed-thinking tasks specifically asking them to generate positive versus negative thoughts. We predicted and found no affective asymmetry and a moderate-sized cognitive positivity bias that declines with practice. The second four of the 10 studies investigate asymmetries in proclivity (or preference beyond ability) that appear when people free associate on a variety of stimuli. As regards proclivity, we predicted and found a large, uniformly positive cognitive bias (that declines somewhat as children mature), but only a slight affective bias that is positive when autistic needs are dominant and negative when realistic needs dominate. A final pair of studies show that the cognitive and affective variables interact as regards how directed positive versus negative thinking about a stimulus affects evaluation of that stimulus.