Function approximation is a central issue in subjects as diverse as pattern recognition , control theory and statistics. Prediction (forecasting) is essential for planning and operation control in a variety of areas such as: production management, inventory systems, quality control, financial, planning, and investment analysis. The objective of this work is to investigate the use of neural networks in Function Approximation, Data Fitting, and Prediction. The counterpropagation network was considered and an attempt was made to enhance its performance. As a result of this work, we propose a new neural network architecture named Single Layer Linear Counterpropagation ( SLLIC ) network. The SLLIC neural net has the following additional features:- Weight Lnithi Hzation. Automatic Structure Determination. Higher Order Neural Network Concepts. A system based on the SLLIC model for Function Approximation, Data Fitting, and Prediction was built with data management system facilities. The system was tested and results show that the performance of the system in terms of good approximation or prediction is better than other neural nets architectures and traditional techniques. The SLLIC system was implemented on an IBM/PC compatible using turbo C 2.0 with Foxpro2 languages.