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Relationships between Ebbsfleet supporters and club staff are being put at risk because of a negative minority on the terraces at away games.
Fleet players chose not to acknowledge their fans after Saturday’s 1-1 draw at Hemel Hempstead following alleged incidents of personal abuse during the match.
The atmosphere on the sidelines was the main topic of conversation in the visitors’ changing room at Vauxhall Road.
Coaching staff and club officials, including secretary Peter Danzey, have also come in for stick and Fleet vice-chairman Peter Varney issued a statement on Monday describing the behaviour of the individuals as "unacceptable" and "aggressive".
He said: "I’m not having it any more. They’ll stop it – or we will.
"I’ve got no problem with criticism – people saying ‘you’re useless, you’re rubbish’ – that’s football.
"But it’s when they start coming up to people, whether that’s (manager) Steve Brown or (general manager) Dave Archer, and start doing it in an aggressive manner.
"I hope they heed the warning. It’s not going to carry on, that’s for sure.
"It affects the players massively. They were talking about it in the dressing room for 15 minutes afterwards. It upsets them. They want to be encouraged, particularly when things aren’t going well. It’s the one thing they don’t want.
"When the whole playing squad doesn’t go over to the fans after a game, you know there’s a problem. We want to create a bond and this is the worst thing they (the fans) can possibly do."
Ebbsfleet are at home to Hayes & Yeading in Vanarama Conference South on Saturday.
Read the full story in the Gravesend Messenger.