Two nephews of Venezuela's first lady confessed to conspiring to import cocaine into the US after being arrested last year, court filings by US prosecutors on Friday said.
Efrain Campo, 29, and Francisco Flores, 30, were arrested in Haiti in November and put on a plane to New York where they are in jail awaiting trial.
Both men have pleaded not guilty.
Their lawyers have argued that their post-arrest statements made during the flight to the US should be suppressed.
They say the defendants did not fully understand their rights under US law to remain silent.
Friday's filings by prosecutors were made to oppose this motion and intended to show that the men were not coerced when they spoke to US Drug Enforcement Administration (DEA) agents.
Prosecutors accuse the defendants of conspiracy to import 800kg (1,760lb) of cocaine into the US from Venezuela, via Honduras.
The case emerged out of a series of investigations by the US authorities, which have linked people connected with Venezuela's political elite to drug trafficking.
It has been an embarrassment for Venezuelan President Nicolas Maduro, whose administration is battling political and economic turmoil.