is mysql 5 able to manage transactions between different users ?

hi !
in mysql doc it is stated that :
"MySQL supports local transactions (within a given client connection) "
ref : http://dev.mysql.com/doc/refman/5.1/en/transactional-command s.html
but what happens if for instance 2 different users tries to modify same
data in 2 different transactions in 2 different connections ?
does the last one which finish simply "win" (erasing the other's work)
or does mysql is able to lock rows in a correct way via transaction
managed locks like oracle/postgrsql/sqlserver/etc. between users' sessions ?
thx & regards,
P.