Software Effort Estimation (SEE) is a procedure to estimate the effort required to develop software. The researchers have been dealing with SEE issues for a long time. Several methods were developed until the formulation of Function Point (FP) and Constructive Cost Estimation (COCOMO) methods. However, these methods were useful only for procedurally developed software, not for modern object-oriented software. On the other hand, using the Use Case Point (UCP) metric acquired from the UML diagrams can be more suitable, as the use case is the fundamental unit of an object-oriented system. An ample amount of research has already been done for UCP prediction using linear regression-based models. However, various nonlinear regression models have not been explored for predicting UCP values from different UCP parameters. Although, some of the researchers have used nonlinear regression models for predicting effort, given the UCP value. Motivated by this, the current work investigates different nonlinear regression models such as a k-nearest neighbor, decision tree, random forest, support vector machine, and multilayer perceptron for UCP prediction. The experimental investigation has been conducted on two publicly available UCP estimation datasets. Further, we compared the performance of nonlinear regression models with the linear regression-based models using different performance measures. The results suggest that the nonlinear regression models perform better than the linear regression-based models.