Eppleton need just eight points to mathematically ensure their Premier Division safety, when they travel to South North to play their final game of the season on Saturday.
Having won promotion from the First Division last season, the Church Road men do not want to return and they hold a healthy 23-point cushion over bottom club Gateshead Fell.
Chairman Jeff Park said: “We just have to go and try and play our best cricket.
“All the players will do their best and, although we have had our fair share of injuries this year, we knew, after promotion last season, that this would be a very difficult campaign.
“The standard of cricket in the Premiership is very high compared to the First Division, but we hope to come out on top after the game, with at least the eight points that are required, but we won’t be playing for a draw. We need to remain positive throughout.”
They will also be hoping that neighbours Hetton Lyons can do them a favour, as they take on Gateshead Fell at Lilywhite Terrace.
The Lyons have had another good season and will probably finish in mid-table, but they will be looking to push South Shields all the way for fifth place.
Fell, meanwhile, quite simply have to win the game, as they have 23 points to claw back and they will be relegated, if they lose or draw.
However, they are seasoned campaigners when the pressure is really on and it promises to be a very interesting game, particularly if Durham paceman Graham Onions plays, as expected.
Fell’s Tom Pinkney is in defiant mood, given the club’s great acts of escapology in recent years and he said: “We still have a chance and everything is still to play for. We have done it in the past and we can do it again.”
Champions Chester-le-Street travel to Newcastle, for what looks like a smashing match to bring down the curtain at Osborne Avenue.
The hosts, who finished third last season, will be hoping to go one better this term and finish runners-up.
They are 18 points ahead of third-placed Tynemouth despite having fallen away of late, allowing the Cestrians to capitalise on their winning run to take the title.
After an explosive start to the season, Newcastle have only won one league game in their last seven, effectively costing them the title this season.
Skipper Jacques Do Toit explained: “We have not done the basics very well at all, in this last third of the season.”
Chester, on the other hand, are flying and have not lost in 10 league games, winning eight of them, with the other two abandoned.
In the other three games, Durham Academy take on Stockton in their last game, Whitburn welcome Tynemouth to the Village Ground to close out their season and South Shields travel to Benwell Hill.