Goldfish, trained in the avoidance shuttlebox with a variant of the linear discrimination procedure, learned to conditionally discriminate between color signals, both for the matching (M) and oddity (O) criterion forms. Transfer to assess the possibility of concept learning was also tested. In original learning, oddity-trained groups learned faster and reached higher conditional discrimination performance levels than did matching-trained groups. In transfer, various groups were tested with the same criterion (MM or OO) or a shifted criterion (MO or OM), and half of each group retained the same color signals and the remaining half had its color signals changed in transfer. Groups with the same criterion in original learning and transfer (MM or OO), regardless of signal colors, showed comparable positive transfer. Groups with their criterion shifted between original learning and transfer (MO or OM) showed comparable negative transfer, regardless of signal colors. Since both positive- and negative-transfer effects were independent of signal colors, it is clear that what was learned for one set of signal colors transferred to at least one other signal-color set. These findings are consistent with the interpretation that goldfish learned the original conditional discrimination at a conceptual level, and learned about the general matching or oddity relationships between colors, rather than about a specific set of colors.