既然是审理(或处理)申诉的案件，应该可以用 “行政申诉程序”。

请参考以下类似用法：

“對公證書的內容有爭議的，根據《公證法》第四十條的規定，可以就該爭議向人民法院提起民事訴訟。司法行政機關不再按行政申訴程序處理有關爭議。”
http://big5.chinalawinfo.com/vip.chinalawinfo.com/newlaw2002...

“本案在2006年3月1日前已完成了行政申诉程序，不应适用《公证法》第四十条之规定，因此不属于民事诉讼的受案范围。”
http://www.tjhp.gov.cn/servlet/ContentServer?cid=11268556878...

“進一步簡化行政申訴程序，以便更有效率地對公共行政機構及公營部門的違法或失當行為及時作出獨立、客觀及公正的調查”
http://www.ccac.org.mo/cn/subpage.php?cat=intro&page=policy&...


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Note added at 1 day23 hrs (2009-07-08 06:20:28 GMT)
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The term "administrative proceedings” (行政程序) is a broad and elusive concept although we usually refer it to “行政诉讼”. From the context Malgorzata Souffez offered, it seems more like “administrative remedies”(行政救济程序) where a complaint may request administrative review of agency decisions (reconsideration of initial determinations). And only the complainant has exhausted available administrative remedies, may he or she resort to the tribunal. And that’s where an “administrative action” (行政诉讼) starts. So we can conclude that “行政诉讼” is the final stage of but does not equal to “administrative proceedings.”

Just like “administrative proceedings”, “administrative remedies”(行政救济程序) are also called differently in different countries of the world:

美国：行政上诉
奥地利、西班牙、意大利：行政诉愿
德国：异议审查
韩国：诉愿
日本：行政不服审查
中国：行政复议程序

Please refer to the following link for detailed (and very helpful) explanation:

http://www.lawbook.com.cn/wsyd/xzcsf/xzcsf-11.htm

Regarding Malgorzata Souffez’s question, I personally feel “行政诉愿程序” and “行政复议程序” should all work. (Literal translation“行政程序”would be too vague; and “行政救济程序”, too specific.)