I think the most commonly used phrase would be "laughing fit" (or "fit of laughter"), where "fit" in this usage means "in a condition of," " or "a state of" something (laughter in this case, but other examples might include coughing or other mostly involuntary conditions).

EDIT: it is interesting to me that the word used in your language is "crisis," as in English that implies something along the lines of an emergency situation requiring immediate attention.