Align:
- If you align yourself with a particular group, you support them because you have the same political aim.
(There are signs that the prime minister is aligning himself with the liberals.)
(He has attempted to align the Socialists with the environmental movement.)
Synonyms: ally, side, join, associate...
https://www.collinsdictionary.com/dictionary/english/align
- Brought into agreement or cooperation on the side of a faction, party, or cause.
https://www.vocabulary.com/dictionary/aligned

Non-aligned Countries — неприсоединившиеся страны, т. е. страны-участники

non-aligned
неприсоединившийся (к союзам, блокам)

align - or a·line[ uh-lahyn ]

a) verb (used with object)
- to arrange in a straight line; adjust according to a line.
- to bring into a line or alignment.
- to bring into cooperation or agreement with a particular group, party, cause, etc.:
For example: He aligned himself with the liberals.

-to adjust (two or more components of an electronic circuit) to improve the response over a frequency band, as to align the tuned circuits of a radio receiver for proper tracking throughout its frequency range, or a television receiver for appropriate wide-band responses.

b) verb (used without object)
- to fall or come into line; be in line.
- to join with others in a cause.