Donald Trump faces a formidable task defending against charges that he illegally kept top-secret documents upon leaving the White House in 2021, according to legal experts, who say neither the law nor the facts appear to be on his side.

The former US president, who is a candidate to run again in the 2024 election, pleaded not guilty in a Florida federal court on Tuesday. The 37 counts against him include violations of the Espionage Act, conspiracy to obstruct justice and making false statements to investigators, a Reuters report stated.

National security law experts were struck by the breadth of evidence in the indictment which includes documents, photos, text messages, audio and witness statements. They said this made a strong case for prosecutors’ allegation that Trump illegally took the documents and then tried to cover it up, according to a Reuters report. Trump’s lawyers did not immediately respond to requests for comment. Trump has called the case a “witch hunt” orchestrated by political enemies.

“There was no crime, except for what the DOJ and FBI have been doing against me for years,” he wrote on his Truth Social platform on Friday in reference to the Department of Justice and the Federal Bureau of Investigation.

Trump’s greatest peril could lie in the conspiracy to obstruct justice charges, which carry a maximum sentence of 20 years in prison, the report added.

Legal experts said the evidence appears to show that Trump was aware he had documents in his possession that were subject to a subpoena but refused to turn them over and encouraged his lawyers to mislead the FBI.

“That’s about as clear a case of obstruction as you could imagine,” said Clark Neily, a legal expert at the conservative Cato Institute.

Obstruction of justice is a particularly difficult charge to defend against, attorney Mark MacDougall said.

Legal experts said Trump’s alleged years-long effort to conceal documents was likely a major factor in Special Counsel Jack Smith’s decision to indict him. During the investigation, Trump’s lawyers told the FBI that they had turned over all classified documents in their possession, which was false. They deny intentionally misleading investigators. The conspiracy element makes the obstruction charges far more serious, and all prosecutors must prove is that Trump worked with another person to try to hinder the investigation, regardless of whether they succeeded. Cato’s Neily said that based on his reading of the indictment, prosecutors probably have many witnesses who have given them similar accounts of Trump’s efforts.

Trump has claimed he declassified the documents before taking them. That assertion is undercut by a taped conversation cited in the indictment, which said Trump showed a secret document to several people and said that he “could have declassified it” as president but did not. But the classification issue will likely end up being irrelevant. Prosecutors charged Trump under the Espionage Act, a World War One-era law that predates classification and criminalises only the unauthorised retention of “national defence information.”

National defence information does not need to be classified to be covered by that law, national security law experts said. The information need only be useful to the nation’s adversaries and be closely held by the government. However, Trump does have some potentially successful strategies. His lawyers could challenge witness accounts, blame others or argue he was following the advice of his attorneys and did not intend to break the law.

If it goes to trial, a Florida jury would hear the case since that is where the special counsel sought the indictment. In the conservative-leaning state, Trump would need only one juror to oppose his conviction for there to be a mistrial. His defence team could also file motions that would delay a trial until after the November 2024 election. Legal experts disagree over whether Trump could pardon himself if he wins.