In this paper, the termination of the following programs is analized. While x?Ω do {x:=f(x)} end. When x is the only program variable, Ω is an interval and f is a continuous function. These are called the Nonlinear Programs over Intervals. This paper shows that the necessary condition for non-termination of the above program is that there is a fixed point of f, either within the interval?Ω, or on the boundary of Ω. Furthermore, if there is a fixed point within Ω, the above condition is not only necessary, but also sufficient. In the case that all fixed points are on the boundary of Ω, it is also possible to construct the corresponding necessary and sufficient condition of non-termination by introducing more constraints for the continuous function f. A piecewise polynomial function meets these constraints, and a decision algorithm for continuous piecewise polynomial function is presented in the paper.