Some English usage authorities urge the use of each other when referring to two people and one another for more than two people. Yet there’s no logical reason for this guideline, and writers break it nearly as often as they follow it. In practice, the two phrases are interchangeable. Here are a few examples from edited publications:
The technology will without doubt change forever how we communicate with each other. [NY Times]
Skirls of grunge guitars, air-horn blasts, reggaeton beats and Clare’s vocals slam against each other so viciously that they burn out. [Guardian]
These are two teams that are not particularly fond of one another. [Wall Street Journal]
Asking about one another’s finances and secret addictions before getting married or moving in together is essential if a couple’s relationship is to last the distance. [Telegraph]
Each other’s and one another’s
When using a possessive form of one of these phrases, the noun that follows should logically be singular (except when the noun really is plural). Consider this example:
The two coaches complimented each other’s team and then started to think about Friday’s challenge. [Sports Ink]
Here, each coach only has one team, so each other’s teams would be illogical.
But that example is a rare exception, and writers usually pluralize the noun—for example:
The proposal would limit cooperation to providing each other’s militaries with essential items. [NY Times]
We who disagree on politics and policy are not each other’s enemies. [CNN]