When at speed, changing lanes or quickly moving side to side is very sloppy, why

[GoGreenMan]

I just got the car the other day and I didn't notice when I test drove it because I didn't really get all that fast. But afterwards when going down the interstate. I noticed that it is very sloppy or loose. almost like it has a flat.
I look at all the tires and one of the back ones was a little low but aired them all up to where they need to be and it fixed a lot of the problem but it is still doing it enough that it worrys me. Please help anyway you can because I have been in Japan for a few years and have also never had a saturn.
some car info...
4dr
75k
stick
and no wierd sounds.
thanks

[PlayStation3]

how fast where you going and it is a front wheel drive car so that you do feel more since the wheels that poviad the pull are like not even a foot away from you and with the tire presurre are they at the factoy spec or atleast have the same psi difference between the front and the back and also if the car is stock those tires are not performance tires so don't treat them like one and since they are small in rubber count 185/65/15 for sl2 and i think ether 175 or 165 for sl1/sl so yea

[GoGreenMan]

I was only going like 60 and it is slopy in the back not because of it being front wheel drive. I think it might be the shocks are old and just not as responsive as they should be.

[PlayStation3]

yea more then likely it sounds like it might beand would go to a place to see if they are going and depending if you do that stuff your self or they just want to much just tell them thats for another time.

[HAWG]

I would check the trailing arms on the rear suspension, along with the rods for the knuckle.

[sierrap615]

i would have a shop look at it, to risky to ignore a steering/supsention problem.

but the SOHC S-seires(SC1,SL,SL1,SW1) do not have a rear swaybar. DOHC models(SC,SC2,SL2,SW2) do, the lack of a rear swaybar will reduce cornering/turning performance, to what extent i do not know, but there is a kit sold to add the rear swaybar to SOHC model, or a spoiler will produce a simular downforce on the rear wheels.