This paper uses a quasi-maximum likelihood procedure to estimate the non-stationary stochastic volatility for the par bonds of four Latin American countries: Brazil, Argentina, Mexico and Venezuela. The aim is to investigate the possible presence of co-movements in volatility across countries. The estimation period goes from August 1994 to September 1999, including, therefore, the Asian and Russian crises. The estimated volatility for the univariate model does not show any slope and is highly persistent. The multivariate model gives a good fit to the data and shows that there is common movement.