The Wiener and Kirchhoff indices of a graph G are two of the most important topological indices in mathematical chemistry. A graph G is called to be a globular caterpillar if G is obtained from a complete graph Ks with vertex set {v1,v2,..., vs} by attaching ni pendent edges to each vertex vi of Ks for some positive integers s and n1,n2,...,ns, denoted by GCs;ni1s. Let GCs;n be the set of globular caterpillars GCs;ni1s with n vertices (n=s+∑i=1sni). In this article, we characterize the globular caterpillars with the minimal and maximal Wiener and Kirchhoff indices among GCs;n, respectively. [ABSTRACT FROM AUTHOR]