Solar and Wind energy based Renewable Energy Systems (RES) are one of the most rapidly growing technologies as a means of producing clean electrical energy. Grid integration of RES involves various types of power electronics-based converters and inverters. These electronic devices produce harmonics at their terminals, which are transferred to the grid. Harmonics forecasting is one of the techniques used to design harmonics mitigation devices in order to reduce harmonics. The core objective of this work is to develop a hybrid forecasting model to produce accurate and reliable harmonics forecasts for RES. Six novel hybrid forecasting models are proposed in this work to perform harmonics forecasting. These models are based on different combinations of multi-layered Artificial Neural Networks (ANN) and Adaptive Neuro Fuzzy Inference System (ANFIS). The forecasting models proposed are two-staged architecture. Three hybrid forecasting models (model-1, 2 & 3) use ANN in the first stage and ANFIS in the second while the other three models (model-4, 5 & 6) are designed vice versa of prior. Two renewable generators are used to generate harmonics. The first generator combines Double-Fed Induction Generator (DFIG) driven by wind turbine with solar photovoltaic (PV) panels whereas, the second generator combines wind turbine driven Permanent Magnet Synchronous Generator (PMSG) with solar panels. The purpose of these generators is to produce voltage and current waveforms using real-world data (Wind Speed & Solar Irradiation). Harmonics are extracted from these waveforms which are used to create training and testing datasets for the forecasting models. Harmonics are forecasted using the six forecasting models proposed and results are validated by comparing them to benchmark work done in the literature. The results show that model-3 and model-6 are the best and most consistent performing models.