This paper presents the first polylogarithmic-competitive online algorithms for two-metric network design problems. These problems arise naturally in the design of computer networks (wired and wireless) as well as many other applications. In most cases the natural applications involve changing sets of communicating nodes, making the online model essential for addressing them. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and ProblemsRouting and Layout; C.2.1 [Computer-Communication Networks]: Network Architecture and DesignNetwork Topology General Terms Algorithms, Design, Theory