动词不定式的完成形式，表示动作早于谓语动词。

一、动词不定式的完成式，不仅可以作状语或补语，例如：

I am only too glad to have been of help to you. 对你能有所帮助十分高兴。

He was later discovered to have been a spy. 后来发现他原来是间谍。

We seem to have wandered from the path. 我们好像已经偏离了原路。

The sea is thought to have been the cradle of life.  人们认为海洋是生命的发源地。

He was lucky to have found a millionaire patron. 他有幸找到了一位百万富翁赞助人。

I feel fortunate to have met them.  我觉得很幸运能见到他们。

Your secret appears to have leaked out. 看来你的秘密已经泄漏出去了。

二、而且，还可以作句子的主语或宾语，例如：

It is quite something to have won him over.  把他争取过来是一件很了不起的事。（动词不定式的完成式作主语）

It was very sharp of you to have noticed that.  你注意到了这一点是够机灵的。（动词不定式的完成式作主语）

He hated to have quarrelled with her.  和她吵了一架,他感到很遗憾。（动词不定式的完成式作宾语）

He claimed to have seen billions of butterflies. 他号称见过无数只蝴蝶。（动词不定式的完成式作宾语）

三、还可以做定语，例如：

Brazil became the fifth country to have hosted the FIFA World Cup twice, after Mexico, Italy, France and Germany. 巴西是在墨西哥、意大利、法国和德国之后，成为第五个两次举办世界杯的国家。（动词不定式的完成式作定语）

【解说】你的句子Hospital staff burst into cheers after doctors completed a 20-hour operation to have separated one-year-old twins at the head.

动词不定式to have separated one-year-old twins at the head 跟上述句子的作用相同，作定语，表示“手术的内容”。表面看，动词不定式 to separate one-year-old twins at the head 所表示的动作，似乎不应早于complete，但是，“分离手术”是一个过程，而“完成”则是终止性动词，瞬间完成的动作，表达一种结果。因此，“过程”应该早于“结果”。

关于动词不定式作目的状语，不可能使用完成式，这是因为目的状语是表达将来的事情。