Many natural events with an S-shaped sigmoidal curve can be well described using sigmoid growth models. Sigmoid growth models are considered one of the most important and most widely used non-linear models in describing the most natural phenomena that have a sigmoidal growth curve in several disciplines such as the physical, chemical, biological, and social sciences.  The purpose of the article is to suggested two new sigmoid growth models using two different techniques based on the Gompertz Exponential ( GoE ) distribution and comparison between them. The parameters of the suggested models are estimated using the maximum likelihood estimation technique. Through a Monte Carlo simulation and application utilizing Egypt's external debt data, the effectiveness of the newly presented models is examined and contrasted with some existing sigmoid growth such as Gompertz, and exponential models to explain the growth. Results showed that the recently suggested Transmuted Gompertz Exponential sigmoid growth model, and Gompertz Exponential sigmoid growth model are better than to the other models