Buxton’s FA Cup second-round tie with Morecambe will be shown live on BBC One, while Yeovil Town’s match with MK Dons or Stevenage will be on BBC Two.
Buxton, who play in the seventh tier of English football, are one win away from joining Premier League and Championship clubs in the third-round draw.
They host League One Morecambe on Saturday, 4 December at 12:45 GMT.
Yeovil’s home tie with MK Dons or Stevenage on the same day (17:30) will be shown on BBC Two and BBC iPlayer.
Six of the 20 second-round ties are being televised live between 3-6 December.
ITV will show Gateshead or Altrincham v Charlton Athletic, Rochdale or Notts County v Sheffield Wednesday or Plymouth Argyle, Salford City v Chesterfield and Boreham Wood v St Albans City.
The FA broadcast fee for this coverage is £60,000 per club.
Buxton, third in the Northern Premier League Premier Division table, are the lowest ranked club left in the FA Cup.
Having started at the first qualifying round stage, they have won five games to reach the second round proper.
Yeovil Town are 15th in the National League.
They will discover their second round opponents on 16 November when League Two Stevenage host League One MK Dons in a first round replay.
Friday, 3 December
Gateshead or Altrincham v Charlton Athletic 19:45 kick-off – live on ITV4
Saturday, 4 December
Buxton v Morecambe 12:45 – live on BBC One and BBC iPlayer
Yeovil Town v MK Dons or Stevenage 17:30 – live on BBC Two and BBC iPlayer
Sunday, 5 December
Rochdale or Notts County v Sheffield Wednesday or Plymouth Argyle 12:15 – live on ITV
Salford City v Chesterfield 17:15 – live on ITV4
Monday, 6 December
Boreham Wood v St Albans City 19:45 – live on ITV4