All cultures, including the dwarves and gnomes, have some form of adulthood rite by which a person makes a transition to adult status. An adult can be oathbound, witness an oathbond ceremony, vote and so forth.
Typically, an age cohort who went through childhood's end rites together will go through adulthood rites together at around the time that the first few members of that cohort begin to exchange promises of oathbond (usually late teens). Among the educated, completion of basic education corresponds with adulthood rites, and this, rather than oathbonding, is the stronger association for most educated people.
The mentally deficient are not granted adulthood rites, and the insane may have them officially reversed.
A pre-adult or "betweener" who, with parental permission, oathbinds (usually because of pregnancy) is generally granted adulthood rites as part of the oathbond ceremony.
See also Childhood's End Rites.