The ancient Greeks understood aristocracy as one of the three pure forms of government.  An aristocracy which had been corrupted was understood to be an oligarchy.  Along with the other types of pure governments were democracy, and monarchy. 

Aristocracy, when corrupted, may also be understood as plutocracy.  And so if there is rule by the few, and the few happen to be wealthy it can be said that the system of government is a plutocratic oligarchy, although this would be better understood simply as a plutocracy.  Staying true to the original meaning of the word aristocracy is difficult however, and the term has come to mean what plutocracy is designed to represent. 

Aristocratic governments imply the use or importance of some kind of assembly of representatives, regardless of how the members are chosen to be apart of such a legislative body.  However there is typically an executive figure in such a government, but his should not take away from the definition of the term.  If the leader is selected because of his or her better qualifications for the job, he or she is understood to be a part of the aristocracy.   It could be said that the United States government is a plutocratic one (though this term is now understood as aristocracy). 

*much of the same definition is used here and for the term "plutocracy" because of the similarities between the connotative and definitive uses of the two words.