The suspect identified as Christian Brueckner is being tried on two counts of rape and two of sexual abuse.
German prosecutors have called for a 15-year prison sentence in the case of a man who is also under investigation in the disappearance of British toddler Madeleine McCann.
The 47-year-old German national, who has been identified by local media as Christian Brueckner, is on trial at the Braunschweig state court in northern Germany over sexual offences he is alleged to have committed in Portugal between 2000 and 2017.
In closing arguments on Wednesday, prosecutor Ute Lindemann argued that the defendant should be convicted of two counts of rape and two of sexual abuse and that he should be kept in preventive detention after serving a 15-year sentence.
Lindemann said he should be acquitted of a third count of rape.
The defence is expected to make its case on Monday, and a verdict could follow on Tuesday.
The suspect is currently serving a seven-year prison sentence in Germany for a rape he committed in Portugal in 2005. He has yet to be charged in the McCann case, in which he is under investigation on suspicion of murder.
He spent many years in Portugal, including in the resort of Praia da Luz around the time of the British toddler’s disappearance there in 2007. He has denied any involvement in her disappearance.
Brueckner’s lawyer said in February that his client wouldn’t respond to the charges, but that he expected an acquittal. There are no formal pleas in the German legal system, and there is no obligation for defendants to respond.
In July, the court lifted an arrest warrant in the cases at stake in the current trial, citing a lack of “urgent suspicion” against the defendant. But he has remained behind bars because of the sentence he is currently serving.