1、keep doing sth. 坚持做某事

强调状态的继续，常与表示延续动作的动词与静止状态的动词连用，如(hope, think, wonder, dream, sit, stand, lie, sleep等)

He kept talking until the meeting was over. 他一直在说，直到会议结束。

He kept eating/ smiling/ walking. 他一直在吃/笑/走。

She keep running 她一直在跑（没停过）

He kept standing in the street .他一直站在大街上。

Please keep sitting where you are.

We’ll keep going forward.

We kept hoping that they would chance to come to china (again) some day.

2、keep on doing sth.表示动作反复，强调动作与动作之间有间隔，常与表示短暂动作的动词连用。 “坚持做某事”，克服困难继续坚持。

He kept on ringing me up, but I don't want to keep in touch with him any more.

他不断地给我打电话，可我不想和他保持联系了。

The boy kept watching the passing traffic at the gate.

这个男孩在门口不停地看着过往的车辆。

She kept on raising her hand 她反复举手（不是一直举着手）

He kept on repeating these words over and over. 他一遍又一遍重复这几句话

keep on doing是指中间有休息停顿的不停地做,比如keep on reading,并不是说一直不停地读书,这期间可以停顿或者已经休息过了等.
而keep doing是指持续不断的,一直保持这个状态keep reading,一直在看书,没有停过,没有休息,没有做其它事.

keep on doing sth.和go on doing sth.在表示都已经停下来了,然后再去继续做这件事的时候,是一个意思,两者都可以用.而keep on doing sth.可以表达的意思比后者要更广泛,如上所述.

go on doing 继续干同一动作，同一事情。除了表示持续不停地进行某一动作外，还可以继续某一中断了的事情。go on强调事件的连续性。keep on 强调事件的重复性，坚决性。

They will go on fighting so long as there are colonies there.

She nodded, smiled and went on stitching.（缝衣服）

You ought not to go on living this way.

go  on+to do/doing/with有什么区别？

 答：go on to do sth.；go on doing sth.；go on with sth.

这三个短语都有继续做某事的意思，但在含义上有所不同。

(1) go on to do sth. 表示“接着做另一件事”，即接下去做与原来不同的一件事；

(2) go on doing sth.表示“继续不停地做某事或间断后继续做原来没有做完的事”；

(3) go on with sth. 表示“间断后继续做原来没有做完的事”，其后一般接代词作宾语。通常情况下，go on doing sth．和go on with sth．可互换。

试比较：

After they had read the text, the students went on to do the exercises．

读完课文后，学生们继续做练习。

The students went on talking and laughing all the way．一路上学生们一直有说有笑。

After a rest, we went on with our lesson（＝After a rest, we went on having our lesson．）．

休息以后，我们继续上课。

keep doing sth./ keep sb. doing sth.

在这两个结构中，keep后有无sb. 意义是不相同的。

(1) keep doing sth. 意为“不断/反复/坚持做某事”，动作是主语本身发出来的。如：

He kept asking us to remember teamwork.他不断地叫我们记住合作。

 (2) keep sb. doing sth. 意为“让某人做某事”，keep在这里有
“使……处于某状态”之意，doing的动作不是主语来完成，而是由宾语sb.来完成的。例如：

I keep them waiting at the gate.我让他们在大门口等候。