This study attempted to account for resurgence on the Peak Procedure using 6 possums (Trichosurus vulpecula) as subjects. The Peak Procedure is made up of randomly mixed fixed intervals (FI) and peak intervals (PI), with the ratio of FI trials to PI trials being 4:1 respectively. Conditions 1-4 were used to replicate Church et al.’s (1991) procedure from their second experiment. The authors found that when the PI trial length was variable, data from PI trials showed that responding did not resurge, as it did when the PI duration was fixed. Condition 1 used a FI 20 s and a variable PI with a mean of 80 s. Responding did not resurge, but rather decreased to a low level throughout the PI trial. Condition 2 used a FI 20 and a fixed PI of 100 s. Responding resurged for this condition. Condition 3 and 4 repeated Condition 1 and 2 respectively to give an ABAB design. Responding again decreased and increased as the PI changed to being variable and fixed respectively. These results are similar to that found by Church et al. (1991), and show support for what Sanabria and Killeen (2007) call the anticipation theory (where escape from a non-reinforced PI trial is negatively reinforcing). The PI duration was shortened to twice the FI length in Condition 5 and lengthened to 300 s, or 15 times the FI in Condition 6. This was in order to investigate whether responding would resurge at very short and very long PI durations. Responding did not resurge at the shorter PI length, and this may be due to there not being enough time to do so. At the extreme length of 300 s, responding was seen to resurge; a result that is not consistent with other studies that used a similar procedure (Sanabria & Killeen, 2007). When the procedure returned to using a FI 20 s and a variable PI with a mean of 80 s in Condition 7, resurgence decreased to a minimum and remained stable till the end of the trial. Results from the present study support Church et al.’s (1991) anticipation theory, and that as long as the animals can track the end of the PI trial, responding will resurge; if it is variable, animals cannot predict the end of the trial and so response resurgence does not occur.