It has long been known that the consensus problem cannot be solved deterministically in completely asynchronous distributed systems, i.e., systems (1) without assumptions on communication delays and relative speed of processes and (2) without access to real-time clocks. In this paper1 we define a new asynchronous system model: Instead of assuming reliable channelswith finite transmission delays, we assume stubborn channels with a finite average response time (if neither the sender nor the receiver crashes), and we assume that there exists some unknown physical bound on how fast an integer can be incremented. Note that there is no limit on how slow a program can be executed or how fast other statements can be executed. Also, there exists no upper or lower bound on the transmission delay of messages or the relative speed of processes. The are no additional assumptions about clocks, failure detectors, etc. that would aid in solving consensus either. We show that consensus can nevertheless be solved deterministically in this asynchronous system model.