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This paper analyzes the performance of multiple steps estimators of vector autoregressive multivariate conditional correlation GARCH models by means of Monte Carlo experiments. We show that if innovations are Gaussian, estimating the parameters in multiple steps is a reasonable alternative to the maximization of the full likelihood function. Our results also suggest that for the sample sizes usually encountered in financial econometrics, the differences between the volatility and correlation estimates obtained with the more efficient estimator and the multiple steps estimators are negligible. However, when innovations are distributed as a Student-t, using multiple steps estimators might not be a good idea. ; Financial support from IVIE (Instituto Valenciano de Investigaciones Económicas) to the project "Estimating Multivariate GARCH Models in Multiple Steps with an Application to Stock Markets" is gratefully acknowledged. We also acknowledge the Spanish Government for grant ECO2011-29751.