This year the first day of בה"ב falls out next Monday which also happens to be ה' אייר, which I thought was Yom Haatzmaut. I was wondering as to what people who usually observe both (e.g. say selichos on בה"ב and say Hallel on Yom Haatzmaut) would do Monday when the 2 clash.
However, I have been informed that according to the present position of the Chief Rabbinate in Israel, when ה' אייר falls on a Monday, Yom Haatzmaut is pushed off until Tuesday. The same applies if it falls out on Friday or Shabbos (it is pushed back to Thursday). ה' אייר is the same day as the seventh day of Pesach. Therefore ה' אייר can only fall out on Friday, Shabbos, Monday or Wednesday. On Friday, Shabbos, and Monday, Yom Haatzmaut is not observed on that day but pushed off, meaning that in reality most of the time it is not celebrated on ה' אייר. This is quite interesting and leads to some strange results, in America many people will celebrate Yom Haatzmaut on Monday ה' אייר while in israel it is officially celebrated on Tuesday.
How this works out with Hallel is a good question.