Support vector machines (SVMs) with the gaussian (RBF) kernel have been popular for practical use. Model selection in this class of SVMs involves two hyper parameters: the penalty parameter C and the kernel width σ. This letter analyzes the behavior of the SVM classifier when these hyper parameters take very small or very large values. Our results help in understanding the hyperparameter space that leads to an efficient heuristic method of searching for hyperparameter values with small generalization errors. The analysis also indicates that if complete model selection using the gaussian kernel has been conducted, there is no need to consider linear SVM.