In this article, we study the relation type of the fiber cone of certain special classes of ideals in Noetherian local rings. We show that in any Noetherian local ring, if deviation of I is 1, and depth (Formula Presented.), then the relation types of R(I) and FL(I) are equal. We also prove that for lexsegment ideals in K[x, y], where K is a field, the relation types of the fiber cone and the Rees algebra are equal. © 2015, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.