We consider the problem of fair resource allocation for multi-carrier systems. Opportunistic scheduling exploits the time-varying, location-dependent channel conditions to achieve multi-user diversity. Previous work in this area has focused on the single-user scheduling in single-carrier systems over a narrowband flat-fading channel, where only one node is scheduled at a time. In wideband multi-carrier systems, multiple nodes can be scheduled concurrently over multiple narrowband channels. In this paper, we analyze proportional fair scheduling (PFS) in multi-carrier systems over a wideband frequency-selective channel. In particular, we first derive analytical expressions for the throughput of opportunistic scheduling under proportional fairness constraints in a frequency-selective channel, for both single-user and multi-user systems. Furthermore, we provide closed-form expression to quantify the throughput benefit of the multi-user PFS over the single-user PFS in frequency-selective systems. This research is an extension of our previous theoretical work on opportunistic scheduling over flat-fading channel in narrowband single-carrier systems.