Johannesburg – The case against terror-accused twins Brandon-Lee and Tony-Lee Thulsie was postponed in the Johannesburg Magistrate's Court on Wednesday.The case was postponed until April 25 for further investigation, National Prosecuting Authority spokesperson Phindi Louw said.She said the State has not yet finalised its investigation.Last Friday their lawyer Annelene van den Heever argued that the case should be struck off the roll and that the State needed to get its house in order."This matter should be struck off the roll and reinstated when the State has more evidence to place the matter back on the roll," she said at the time.Magistrate Pieter du Plessis reminded her of the seriousness of the case.‘Linked to Islamic State’Van den Heever was objecting to the State's request for a postponement to allow for further investigations.The twins were arrested in July last year during raids in Newclare and Azaadville, on the West Rand. They face three counts of contravening the Protection of Constitutional Democracy Against Terrorist and Related Activities Act.According to their charge sheet, the brothers, who were arrested along with siblings Ebrahim and Fatima Patel, were allegedly linked to the self-proclaimed Islamic State and were allegedly planning to set off explosives at a US embassy and "Jewish institutions" in SA.Prosecutor Chris MacAdam said the twins chose to abandon their bail applications in October."They cannot complain that they are unlawfully kept in custody," MacAdam said.MacAdam said the State had a strong case. The investigating officer had found a press statement relating to the terror attacks in Paris in November 2015 on one of twins' devices. He did not say who had issued this statement.International investigationThey had found a document, "Mujahid Guide 2015 - How to survive in the West", on one of the devices. A mujahid is one who is engaged in the act of jihad.On Tuesday, MacAdam told the court that the investigating officer had discovered that prior to their arrests the twins had been active on social media allegedly discussing matters that could incriminate them.He said the arrests of two suspects in Kenya and Britain were allegedly linked to the case against the twins.MacAdam said US authorities also had jurisdiction over the case and had registered a local case, and would subpoena service providers. He did not elaborate. He said senior British officials had met the investigating officer.The State had approached the Syrian and Turkish governments because there was information that the twins had wanted to go to Syria, MacAdam said.