Abstarct: In this thesis, the aim is to estimate the nonparametric part of semiparametric models by multivariate adaptive regression splines (MARS) and smoothing splines, where the former is used as an adaptive spline while the latter is non adaptive. By the help of explaining scatterplot smoothers and concept of splines, the two aforementioned methods, MARS and smoothing spline, are described in details. And the use of these two methods is described in the estimation process of semiparametric models. Comparison is then done by simulation and applying to several real world examples. After utilization each of these two methods, it is clearly shown that adaptive splines performs better in the sense of having larger R-square and smaller residual sum of squares.