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предъявлять претензии stresses
gen.	be critical of (someone – к кому-либо msn.com Tanya Gesse); complain; have grievances (wikipedia.org Tanya Gesse); claim; set up (на что-либо-for)
busin.	lay claim to
disappr.	make a fuss (The NCB didn’t want to investigate the problem and basically suggested that if the town made a fuss, the mine would be closed and that would be an economic catastrophe.” mysteriousuniverse.org ART Vancouver)
econ.	prefer to prefabricate claims; prefer claims
IT	bid
Makarov.	make claims; raise claims; raise demands
предъявлять претензию
gen.	raise a claim (a demand, etc., и т.д.); claim; lay a claim to (на что-либо); lay challenge to (на что-либо); pursue a claim (Irina Verbitskaya)
busin.	assert; demand; put in claims; assert a claim; file a claim; lodge a claim; make a claim; present a claim; raise a claim; set up a claim; claim default
dipl., law	assert (на что-либо)
econ.	reclaim; lay a claim
law	set up аdefence (Право международной торговли On-Line)
Makarov.	lay a claim to something (на что-либо); lay challenge to
torped.	put forward a claim; lodge a claim (кому-либо, with smb.)
USA	have a problem (with somebody; slang Maggie)
предъявлять кому-либо претензии
gen.	pick a bone with
Makarov.	pick a bone with (someone); hold a demand against (someone)
предъявлять кому-либо претензию
law	hold a demand against (someone Право международной торговли On-Line)

предъявлять претензии: 21 phrases in 10 subjects

Accounting	1
Advertising	1
Aviation	1
Business	5
Economy	1
General	5
Insurance	1
Law	4
Makarov	1
Technology	1