A folyamat vége közel van.

• a = the
• folyamat = process
• vége = its end / the end of it
• közel = near / close
• van = is

So the structure is literally something like:

The process its-end near is.

Natural English: The end of the process is near.

Because vége is the possessed form of vég (end).

In Hungarian, instead of saying the end of the process with a separate word like of, you often make the possessed noun show the relationship:

• vég = end
• vége = its end / the end of it

So:

• a folyamat vége = the process's end = the end of the process

This is a very common Hungarian pattern.

This is a possessive structure.

Hungarian often expresses X of Y as:

Y + possessed X

So:

• a ház ajtaja = the door of the house
• a könyv címe = the title of the book
• a folyamat vége = the end of the process

Here:

• a folyamat = the process
• vége = its end

Notice that the possessor (a folyamat) does not need any special word like English of.

That's a very common question.

Hungarian usually omits van (is) in the present tense when describing something with a noun or adjective:

• A ház nagy. = The house is big.
• A könyv érdekes. = The book is interesting.

But with certain expressions of location, state, or words like közel (near), Hungarian often uses van naturally:

• A bolt közel van. = The shop is near.
• A megoldás kéznél van. = The solution is at hand.

So in A folyamat vége közel van, van sounds normal and expected.

Here közel means near / close.

It behaves a bit differently from a typical adjective in English. In Hungarian, közel can function in ways that overlap with English near, close, and sometimes closely depending on the sentence.

In this sentence:

• közel van = is near

So:

• A folyamat vége közel van. = The end of the process is near.

Yes, that is a very natural interpretation.

The literal meaning is:

• The end of the process is near.

But in normal English, that often becomes:

• The process is almost over.
• The process is nearing its end.

So even though the Hungarian sentence talks about the end, the practical meaning is often that the process will finish soon.

Yes, Hungarian word order is flexible, but changes in order often affect focus or emphasis.

Neutral order:

• A folyamat vége közel van.

This sounds like a straightforward statement: The end of the process is near.

You might also hear:

• Közel van a folyamat vége.

This puts a little more attention on közel van (is near), and in many contexts it sounds just as natural.

So both are possible, but the original sentence is a clear neutral way to say it.

Because a folyamat vége is a single possessive phrase: the process's end / the end of the process.

The definite article belongs to the possessor phrase:

• a folyamat = the process

Then vége already carries the possessive idea (its end), so you do not add another article before vége in this structure.

Compare:

• a folyamat vége = the end of the process
• not a folyamat a vége in this meaning

Very often, yes.

Some useful examples:

• a film vége = the end of the film
• a nap vége = the end of the day
• a történet vége = the end of the story

Also, vége van is a very common expression meaning it is over / it has ended:

• Vége van. = It is over.
• A filmnek vége van. = The film is over.

So vég / vége is an important word family to learn.

Yes. Depending on style, you could also say things like:

• A folyamat hamarosan véget ér. = The process will end soon.
• A folyamat a végéhez közeledik. = The process is approaching its end.
• A folyamat majdnem véget ért. = The process has almost ended.

Your original sentence is a simple, natural way to express the idea that the process is nearing completion.