Dover's match at Barrow has had to be called off due to a rail incident near Milton Keynes which affected trains.
The incident, between Milton Keynes Central and Watford Gap, caused major delays to services heading north out of Euston.
Lines were shut down, and although they have now reopened, delays are expected until 5pm.
Dover initially put out a tweet saying they were delayed but at 1.45pm it was announced the fixture had been postponed.
Stockport's home game with Dagenham & Redbridge, and AFC Fylde versus Sutton were also called off.
A statement from National Rail said: "The emergency services have dealt with the incident between Watford Junction and Milton Keynes Central, allowing all lines to reopen.
It added: "Trains are subject to delays of up to 90 minutes with some trains cancelled or amended."
A statement on the National League's website explained: "An emergency railway incident took place near Milton Keynes Central, which caused major disruption to departing northbound trains from London Euston.
"As a consequence, the travelling parties of Dagenham & Redbridge, Dover Athletic and Sutton United were severely delayed in their journeys.
"Following consideration for alternative arrangements, matches at Stockport County, Barrow and AFC Fylde were postponed.
"Bromley continued their journey to Solihull Moors, and the Clubs and Match Referee were able to arrange for the fixture to take place at a later time (the game kicked-off at 3.15pm).
"The National League is disappointed to learn of the postponements, offering it's sympathies to all supporters and the Home Clubs involved, particularly with today's celebration of Non-League Day.
"Rearrangements for the three MANarama National League matches will be made in due course."
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