I believe the intended meaning is along the lines of:

'Hungarian universities which require language exit examinations accept the Euroexam'

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Note added at 1 hr (2012-04-13 00:45:37 GMT)
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hi bakopeter, another possible option for the idea of 'accept' here, if that idea is confirmed, would be 'recognize/recognise the...'

I hope this helps

Maybe they mean "Hungarian universities which have language exam exit requirements accept the Euroexam."

Just a guess.

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Note added at 11 hrs (2012-04-13 11:18:53 GMT)
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Glad I could be of help. Good luck on the rest of your exam!

Now that you've provided some more explanation, I believe these two words need to be replaced: "witch" > WHICH and "except" > ACCEPT.
Witch: "one that is credited with usually malignant supernatural powers; especially a woman practicing usually black witchcraft" (would not make sense here)
*Which*: being what one or ones out of a group —used as an interrogative (e.g. "kept a record of which employees took their vacations in July");
Except: "with the exclusion or exception of" (would not make sense here)
*Accept*: "to recognize, to give admittance or approval to, to regard as proper" (e.g. "only written applications are accepted")

Euroexam provides services in language studies and the successful passing of their language test will be considered acceptable by most Hungarian universities where a pass grade in a language exam is an exit requirement. See their homepage, and a few related references from this field.

Euroexam FAQ:
http://www.euroexam.org/gyakori-kerdesek
"Elismert nyelvvizsga
Államilag elismert a vizsga?
Igen. Felvételihez, diplomához, karrierhez ma már nélkülözhetetlen az államilag *elismert* nyelvvizsga. Az Euroexam nyelvvizsgákat teljes értékű angol ill. német nyelvvizsgaként használhatod a felvételinél (a mindenkori pontértékeknek megfelelően), a diplomához, és természetesen *elfogadják* álláskeresésnél is.
Ez azt jelenti, hogy az Euro és EuroPro a felvételitől a diplomán át a nyelvpótlékig mindenütt *érvényes*, államilag *elismert* nyelvvizsgáknak számítanak."

CEF homepage:
http://www.examenglish.com/CEFR/cefr.php
"The Common European Framework of Reference for Languages (CEF or CEFR) was put together by the Council of Europe as a way of standardising the levels of language exams in different regions. It is very widely used internationally and all important exams are mapped to the CEFR."

French language school, glossary:
http://www.frenchfaster.com/glossary.htm
ENTRY REQUIREMENT: Your second language (B1 level)
*EXIT REQUIREMENT*: Your third language (A2 level)

INSEAD - "The Business School for the World"
Language Policy:
http://mba.insead.edu/admissions/documents/language_policy.p...
"The *exit requirement* may be certified in one of the following ways:
• by taking a written test with FL&C or RELC during the first week of the programme (referred to as orientation week), or
• by using the same means available for validating the entry requirement as detailed in Section 3.3 before or during the programme. ...
Language test during Orientation Week (the first week of the programme)
To validate the *exit requirement*, written tests** are held during the first week of the programme. Please refer to Annex 2 for the list of language tests available. Registration for the test takes place on Entry Day and test fees are listed in Annex 1.
** In some rare instances, the *exit requirement test* may be based on an oral interview and a reading-comprehension test only. As there are no written elements to evaluate, a practical level is the minimum required score to validate the *exit requirement*. Please be aware that for some languages, the test may be conducted by telephone."
- - -

I find it rather surprising that the term "exit requirement" had so many colleagues puzzled... I thought it was fairly straightforward and common in English. Here is another example, hopefully it will shed some light on the term for those still in doubt:

"Academic Policies Listing | Catalog Table of Contents | Index
USF 1997-98 Undergraduate Catalog - Pages 46 - 48

*EXIT REQUIREMENTS*

(Part of the Liberal Arts Requirements)
(9 Semester Hours)

Major Works and Major Issues: A portion of the *exit requirements* consists of a minimum of six (6) semester hours of approved coursework concerning major works and major issues. Courses will focus on major issues, documents, or works, and will allow students to read primary texts. These courses may allow students to delve into topics on an interdisciplinary basis. Students will be encouraged to write enough to fulfill Gordon Rule requirements. At least one of the Major Works and Major Issues courses will be taken outside the student's major discipline(s) and may, with the consent of the instructor, be taken for S/U credit.
...
Literature and Writing: In addition, students will take three (3) semester hours of approved *exit requirement* coursework in literature and writing. These courses will allow students to read significant literature of the world and write at least 6,000 words. Significance of the literature will be determined by the department offering the course. The 6,000-word requirement meets Gordon Rule requirements and is for students who may wish to satisfy some of this requirement with upper-level courses. The writing requirement may be satisfied with assignments that include, for instance, revision and rewriting, and process writing. This requirement may be satisfied through comparitive literature courses. These literature courses need not be limited to the English Department. The course may be taken within the major if appropriate.
...
All students must achieve an overall average of "C" (2.0GPA) in the lower level requirements and a grade of "C" or better in each of the *exit requirement* courses. Students will take at least one of the Major Works and Major Issues courses outside their discipline(s). This course may be taken for S/U credit, with the consent of the instructor. Only courses numbered 3000 or above may be used to satisfy the *exit requirements*. *Exit requirements* must be taken at USF.

Although post-secondary foreign language courses may not be required for all graduates, students are encouraged to become competent in at least one foreign language. Foreign language study enriches the command of English, enlarges cultural perspective, and enhances learning skills.

All courses listed are certified as meeting the *Exit requirement* as of April, 1997. Additional courses may have been certified since that date. Please consult with an academic advisor for current and additional information."

http://www.ugs.usf.edu/catalogs/9798/LAEXIT.HTM

Ordinarily, I would change "which" to "that" and "except" to "accept," as follows (and as suggested by others):

Hungarian universities that have language exam exit requirements accept the Euroexam.

Since you said these answers are not working, however, perhaps you could try "having" as follows:

Hungarian universities having language exam exit requirements accept the Euroexam.