In this study, anaerobic co-digestion of apple pulp (AP) with high carbon content and chicken manure (CM) with high nitrogen content was evaluated with regard to sulphuric acid pretreatment conditions in the concentration range of 1%-6% v/v. The best mixing ratio of CM:AP was determined as 3:1 w/w under untreated conditions for which the methane yield was 255.88 +/- 11.55 mL/g VS (volatile solid). Sulphuric acid pretreatments were applied to this mixture ratio. The highest methane yield after pretreatment was 466.01 +/- 10.85 mL/g VS in the reactor, where the sulphuric acid pretreatment concentration was 3.0% v/v. Control of acid pretreatment results were achieved by analysis of lignocellulosic degradation and increase in soluble chemical oxygen demand. The highest cellulose, hemicellulose and lignin degradation after pretreatment were 27.5% +/- 1.4%, 35.9% +/- 2.9% and 14% +/- 1.5% w/w, respectively. The cumulative methane yields (CMY) were analysed by the modified logistic model, modified Bertalanffy model (MBM), modified Gompertz model (MGM) and modified Holling model (MHM). The MBM and MGM were found to fit the experimental data better than other models. The MHM has not previously been applied to CMY. In addition to the kinetic studies, new critical points for CMYs were identified in the logistics model (lm). The importance and critical properties of these points with regard to CMY are introduced. The differences and superior properties of these critical points compared to other modelling methods are discussed.