West Yorkshire Police said there were no grounds to charge the men, aged 52 and 21 and from Dewsbury, after they were arrested on Tuesday.
Police said an investigation was continuing after the men were released last night.
Chief Superintendent Steve Cotter, said: “I’d like to thank local residents for their support and patience over the last few days, which have understandably caused some concern within our communities.
"Public safety remains our utmost priority and I want to offer my reassurance that we will continue to serve and protect the public of Kirklees.
“As always, we would encourage people to come forward if they have concerns about suspicious activity.
"We work very closely with our colleagues at Counter Terrorism Policing North East and are committed to ensuring that any information we receive continues to be acted upon quickly and efficiently.”