We study the fairness of TCP Vegas. The latter is an alternative to the commonly used TCP Reno, and uses measures of the round trip time as feedback on congestion. We consider two cases that depend on the value of the two parameters $\alpha$ and $\beta$ controlling the window sizes' update. Our main conclusion is that TCP Vegas is unfair in several points. First, when $\alpha = \beta$, if the propagation delays are correctly estimated, TCP Vegas is known to be fair. However we show that any over-estimation of the propagation delay of a given connection results in an increase of its rate and hence leads to unfairness. This rate increase augments with the over-estimation factor. Moreover, the rate oscillations, whose amplitude increases with the rate value, are not sufficient to provide an accurate estimation of the propagation delay. Second, when $\alpha<\beta$, TCP Vegas is unfair even if the propagation delays are correctly estimated. In this case, the rate of a connection converges to a stable value that depends on the arrival order of all connections so that earliest established connections get more bandwidth. Also, in a more realistic scheme, later connections see their propagation delay over-estimated and thus they gain larger portion of the bandwidth. These two effects tend to counterbalance each other but the second tends to dominate. Future use of TCP Vegas in the context of TCP-friendly applications, should therefore rely on $\alpha=\beta$, but will require the propagation delays to be correctly estimated. Yet, this seems to be quite hard to achieve.