Enormous Internet growth is an obvious trend nowadays while Internet protocol version 4 address space exhaustion led into the invention of Internet protocol version 6 and subsequently raised the transitioning challenges from one protocol to the other one. As the Internet protocol version 6 have not been around for a long time, thus there is a limitation knowledge in topology, routing change and performance of IPv6. Several studies are going on in order to getting the information about IPv6 which makes a contribution with improvement and deployment of IPv6 and accelerates this transitioning which one of the aspects is the Internet path stability. With this aid this thesis proposed a comparative study of Internet path stability over IPv4 and IPv6. First a measurement of Internet paths over both IP versions has been performed, then the Internet path changes have been extracted in each single set of source-destination pairs. Finally some analysis on the data has been performed in order to observe the stability of Internet paths and provided a comparative study in the set of IPv4 and IPv6.