The former top the standings on goal difference at the moment, while the latter sit second.
At the other end of the table, meanwhile, there are three teams with a different and seriously unwanted 100 per cent record - with them having lost all three of their games so far. Those three teams are Mallbackens IF, Kristianstads DFF and Djurgardens IF.
It's about breaking and maintaining streaks this time out, with plenty at stake as teams aim to get off to the best possible start in these early weeks.
Three out of three?
Linköping certainly have a difficult task in maintaining their winning start this week, as they face Eskilstuna United on Thursday evening.
United have been tipped as strong title contenders along with Linköping and Rosengård, and so tomorrow night's encounter will be a big test of their credentials as they look to bounce back from last week's defeat to Vittsjö GIK.
Rosengård, meanwhile, don't face Piteå IF until Wednesday, giving the current leaders the chance to go three points clear at the top of them and put all the pressure on the current champions.
Piteå are dark horses for the title, or at least a UEFA Women's Champions League spot, this year after last season's third-place triumph. With talent aplenty in their squad, they can certainly trouble Rosengård, who are in delayed action due to tonight's Svenska Cupen quarter-final with Vittsjö.
None out of three?
While the top two will see the need for victory as big this week, it's even bigger for the bottom three.
Djurgården are the side bottom of the league heading into the third week, with them having scored the fewest goals of the three, who are all tied on a goal difference of minus four. This week, they will host Vittsjö, hoping to take advantage of the fact that they are down to play tonight in the cup before travelling on Sunday.
Vittsjö have won one and drawn one of their fixtures so far, while a place in the last four of the cup is on the cards too. They've brought in a lot of talent over the off-season to compensate for plenty lost, and have the players that can make the difference in tight games.
Djurgården will really need to take their chances when they get them, looking to score just their second goal of the season.
Kristianstad, occupying the second relegation spot, have the task of hosting KIF Örebro this weekend. A club touted to have a strong season, Örebro have drawn their first two games and so this game sees two sides go head-to-head in search of their first win of the new campaign.
KIF's defence has been impressive so far, but this week the onus is on their attack to get the job done as they look to breach a Kristianstad back line that has already conceded six goals in just two games.
Finally, Mallbacken will travel to Umeå IK in another battle between two teams without a win yet in this new season. The former have conceded the most goals in the league after two games, with seven leaked, but they do have promise going forward that teams around them haven't shown yet.
Umeå have drawn both affairs so far in 2016 and have been uninspiring at both ends, but will see this game as an opportunity to get the monkey off their back and secure their first win.
The sixth and final side looking for their first victory is Göteborg FC, who visit Kvarnsvedens IK on Sunday. The latter are in an early fourth place in the standings and have been impressive so far with a win and a draw, while their opposition have struggled to get off the mark.
Kvarnsveden will be looking to continue to build momentum then after a bright start.