ＩＭＨＯ：

Ｙｏｕｒ　ｏｗｎ　ａｎｓｗｅｒ　ｉｓ　ａｌｓｏ　ｔｏ　ｔｈｅ　ｐｏｉｎｔ，　ａｌｔｈｏｕｇｈ　ｂｙ　ｓａｙｉｎｇ　‘三级急性病’　ｍｉｇｈｔ　ｍｉｓｓｌｅａｄ　ｐｅｏｐｌｅ　ｔｏ　ｔｈｉｎｋ　ｔｈｅｒｅ　ｅｘｉｓｔｓ　‘一级，二级急性病’　ｗｈｉｃｈ　ｉｓ　ｎｏｔ　ｔｈｅ　ｃａｓｅ　ｈｅｒｅ．　Ａｎ　＇ａｃｕｔｅ　ｔｅｒｔｉａｒｙ＇ｃａｒｅ　ｉｓ：
＂ expertise focuses on care delivered in acute and critical care settings. ＂（http://www.pitt.edu/~rwf15/）

Ｉ　ｔｈｉｎｋ　ｉｔ　ｉｓ　ｃｒｕｃｉａｌ　ｔｏ　ｓｅｐｅｒａｔｅ　＇ａｃｕｔｅ＇ａｎｄ　＇ｔｅｒｔｉａｒｙ＇ａｓ　ｔｗｏ　ｓｅｐｅｒａｔｅ　ｓｉｔｕａｔｉｏｎｓ，　ｙｏｕ　ｃａｎ　ｃｈｏｏｓｅ　ｔｏ　ｔｒａｎｓｌａｔｅ　ｔｈｅ　ｍｏｓｔ　ａｐｐｒｏｐｒｉａｔｅ　ｗａｙ　ｙｏｕ　ｔｈｉｎｋ．　Ａ　ｍｅｄｉｃａｌ　ｃｅｎｔｒｅ　ｗｉｔｈ　ａｃｕｔｅ　ｔｅｒｔｉａｒｙ　ｃａｐａｃｉｔｉｅｓ　ｍｅａｎｓ　ｉｔ　ｈａｓ　ａ　ｇｒａｎｄ　ｓｃａｌｅ　ｆａｃｉｌｉｔｉｅｓ．　Ｐｒｏｂａｂｌｙ　ｓｉｍｉｌａｒ　ｔｏ　国内的三级医院ｗｉｔｈ急诊病房．
　

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Note added at 26 days (2006-05-30 08:48:02 GMT) Post-grading
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Good question, Han Li. In principle, 'acute' could also be a modifier, why not--as Chinese Concept suggested. I don't know the answer, I can only tell you how I approached your question. My first reaction towards 'acute tertiary' was a tertiary hospital with emergency department (instinct). Then to varify my thought, I googled the term with "" on, the outcome was promising. Then I read upon couple of hits (particularly with .gov;.org;.edu etc) which further confirmed my thought. Then to be sure, I googled 'non-acute' vs 'acute' care. That was how I reached my decision.
It is however always beneficial to think outside of the box, thanks!