Az ügyintézési határidő egy hét.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

The next word is ügyintézési, which starts with the vowel ü, so Hungarian uses az.

Compare:

• a ház = the house
• az iskola = the school

So Az ügyintézési határidő... is exactly what you would expect.

Ügyintézési is an adjective meaning something like administrative, processing, or related to handling a case/matter.

It comes from:

• ügy = matter, case, affair
• intézés = handling, managing, processing
• ügyintézés = administration / case handling / processing
• ügyintézési = administrative / processing-related

The ending -i is very common in Hungarian for turning a noun into an adjective.

For example:

• iskola = school → iskolai = school-related
• Budapest → budapesti = from Budapest / Budapest-related

So ügyintézési határidő means processing deadline or administrative deadline.

Yes, határidő is one word, and Hungarian often forms compounds like this.

It is made up of:

• határ = boundary, limit
• idő = time

Together, határidő means deadline.

This is very typical Hungarian word formation: instead of using several separate words, Hungarian often combines them into one compound noun.

In Hungarian, the verb to be is usually omitted in the present tense, third person when linking a subject and a noun/adjective.

So:

• Az ügyintézési határidő egy hét. = The processing deadline is one week.

But Hungarian does include the verb in other persons:

• Én fáradt vagyok. = I am tired.
• Te fáradt vagy. = You are tired.
• Ő fáradt. = He/she is tired.

So the missing is is completely normal here.

Egy can mean both a/an and one, depending on context.

In this sentence, it is most naturally understood as one:

• egy hét = one week

That is because it gives a specific duration. In English, we also say The deadline is one week or more naturally The deadline is one week long / The processing deadline is one week.

So here egy is really functioning as the number one, not just an indefinite article.

Because egy hét is the predicate noun phrase after the subject, and in this kind of sentence Hungarian leaves it in the nominative/basic form.

Structure:

• Az ügyintézési határidő = the subject
• egy hét = the predicate complement

No special case ending is needed here.

Compare:

• A szünet két hét. = The break is two weeks.
• A tanfolyam három hónap. = The course is three months.

Hungarian often uses a bare noun for lengths of time in this structure.

Yes, Az ügyintézési határidő egy hét. is a neutral, straightforward sentence.

Basic structure:

• Az ügyintézési határidő = topic/subject
• egy hét = new information about it

Hungarian word order is flexible, but it is strongly connected to focus and information structure.

This version simply states the fact. If you changed the order, the emphasis could change. For example, putting egy hét into focus position would make the duration more contrastive or emphatic.

So this sentence is the normal neutral way to say it.

A rough guide:

• ügyintézési ≈ uuy-in-tay-zay-shee
• határidő ≈ ha-taa-ree-doe

A few important points:

• ü is like the German ü or the French u in tu
• gy is a single Hungarian consonant sound, somewhat like a soft dy
• é is a long ay-like vowel
• á is a long open a
• ő is a long version of ö

Also, Hungarian stress is always on the first syllable of each word:

• Ügyintézési
• HAtáridő

Because Hungarian adjectives normally come before the noun they describe.

So:

• ügyintézési határidő = processing deadline

This is similar to English in this case. But Hungarian often builds very long noun phrases with adjectives and compounds before the main noun.

The head noun here is határidő.
The word ügyintézési describes what kind of deadline it is.

Yes, depending on style and context.

For example:

• Az ügyintézési határidő egy hétig tart. = The processing period lasts for one week.
• Az ügyintézés határideje egy hét. = The deadline for processing is one week.

The original sentence is compact and natural, especially in administrative or formal language. Hungarian often prefers short, noun-based expressions in this kind of context.

They are closely related, but the structure is different.

1. ügyintézési határidő

   • literally: processing deadline
   • adjective + noun structure

2. az ügyintézés határideje

   • literally: the deadline of the processing
   • noun + possessed noun structure

The second form uses possession:

• határidő = deadline
• határideje = its deadline / the deadline of it

Both can be natural, but the first is often more compact, while the second can sound slightly more explicit.

Yes, it sounds fairly formal or administrative because of words like ügyintézési and határidő.

You are likely to see this kind of sentence in:

• official notices
• websites
• forms
• customer service information
• government or business communication

In everyday conversation, a speaker might choose a less technical wording depending on the situation. But the sentence itself is completely natural Hungarian.