each other and one another

1. Each other and one another mean the same.

• Mary and I write to each other/ one another every day


• They sat without looking at each other/one another.

2. There is a possessive each other's/ one another's

• We often borrow each other's clothes.


• They stood looking into one another's eyes

Each other/ one another are not used as subjects

• We must each listen carefully to what the other says
  (NOT we must listen carefully to what each other say.)

3. Note the difference between each other/ one another and
ourselves/yourselves/themselves.

Compare:

• They were looking at each other
  (= Each person was looking at the other)


• They ware looking at themselves
  (= Each person was looking at him or herself)