My DS2 found a link for knitting a Mobius band and asked me to take a look at it. He was planning on knitting it, but it turned out a little too difficult for a beginning knitter.
As I was reading the directions (Method 1), I thought to myself that the band could be worked even more easily with interchangeable circs.
Cast on the desired number of sts using a Turkish cast on (over 2 circs). (In the pic, I wrapped the yarn around the circs 126 times, for the pattern I was going to make.) Then knit back (or k1p1 back) over those stitches (for the example, 126 sts). These stitches form the "soul" or center of the band. (I placed markers every 18th st because the pattern I was going to use has a repeat of 18 sts.)
Then working with the part of the band away from the loose end, take off the needle tip and the cap. Place the needle tip where the cap was and the cap where the needle tip was. The pic shows the band after the exchange. Lay the work out so nothing is twisted (as in the pic).
Mark the beginning of the round and begin knitting whatever pattern you've chosen for the band. There will naturally be a single twist in the work. Work in pattern until you've knitted all the sts off the circ (126 sts). All the sts (all 252 of them) are now on the same circ.
Replace the cap on the circ that has all the sts on it with a needle tip. Then finish the round (126 more sts for a total of 252, for the example). Continue to knit in pattern. The second pic is of a finished Mobius band, May Flowers Mobius.
A picture of the first Mobius band I knitted is here. It's the last pic in the post. It was knit with worsted weight cotton yarn.
Note: The first pic here shows 2 circs of equal length. It works out better to have the circ on which the "soul" is knitted to be a bit longer since it will eventually be the only circ in use and have to be long enough for twice the "length" of the band.