Dealing with Hungarian authorities, some documents (e.g. business related papers, like set up/dissolve corporation in particular) may need to be legalized by a foreign (non-Hungarian) notary public. Then those documents need to be “superlegalized” by a Hungarian official (consuls, honorary consuls, etc.,) to be valid.
In most of the private dealings (pension transfers, opening bank accounts, power of attorneys to buy/sell real estates) with Hungarian institutions, there is no need to use a foreign lawyer/notary public. They only require a Hungarian official to authenticate documents; to verify signatures and to identify a person.

