Correlated Residuals across equation

[learner]

Dear All

I am using EVeiws 6. In Eviews User Guide II, chapter 33, System Estimation Methods, page 308,

The User Manual does talk about contemporaneous correlation in the errors across equation when it talks about SUR, 2SLS and 3SLS, but when it comes to GMM the Manual is silent about it. So my question is

Does GMM take into account contemporaneous correlation in the residuals?. That is residual of first equation are correlated with the residual of the second equation. The manual is silent. What is your reading about the issue?

Thanking you in advance