In this article I use the lens of Bombay/Mumbai's taxi trade from the early twentieth century to the present to examine how obsolescence becomes ingrained in the political and public imagination, and how this can illuminate the contradictory experiences of time in changing cities. Based on a labor‐centric approach to transport infrastructure, I ask what happens when particular technologies and linear understandings of progress rooted in obsolescence pass over or attempt to erase certain urban subjects. How are these temporal contradictions manifested, and what kinds of political and value claims emerge as a result? Further, how do people actively produce other time‐spaces using alternative temporal claims to challenge progress‐oriented development narratives? How, in other words, does obsolescence resist becoming obsolete? Finally, I examine the role that materiality and physical objects such as cars play in mediating these temporal relationships.