Baud-rate blind equalization algorithms may converge to undesirable stable equilibria due to different reasons. One is the use of FIR filter as an equalizer. It is proved in this paper that this kind of local minima exist for all blind equalization algorithms. The local minima generated by this mechanism are thus called unavoidable local minima. The other one is due to the cost function adopted by the blind algorithm itself, which has local minima even implemented with double infinite length equalizers. This type of local minima are called inherent local minima. It is also shown that the Godard algorithms [10] and standard cumulant algorithms [6] have no inherent local minimum. However, other algorithms, such as the decision-directed equalizer and the Stop- and-Go algorithm [17], have inherent local minima. This paper also studies the convergence of the Godard algorithms [10] and standard cumulant algorithms [6] under Gaussian noise, and derives the mean square error of the equalizer at the global minimum point. The analysis results are confirmed by computer simulations.