The men appeared before Chief Magistrate Ann McLennan on Friday and were remanded to Prison until May 30.
The two men from the Islamic Republic of Mauritania entered Guyana illegally at Springlands, Berbice on May 21.
Ifra Diallo, 25 and Moussa N’Digue, 29, who are from the Northwestern Africa country, were charged separately. It is alleged that they entered Guyana by sea and failed to present themselves to an immigration officer.
Through an interpreter, the two French-speaking men pleaded not guilty to the charge.
Police Prosecutor Gordon Mansfield objected to the men being granted bail on the grounds that they are flight risks.
The men were remanded to prison and matter transferred to the Springlands Magistrates Court for May 30.
There are reports that the men are living in French Guiana. They reportedly board a boat from Suriname and came to Guyana.