If something keeps happening and won't stop happening, we say that it is "continuous" or "incessant". In Chinese, the words are "不断" (bùduàn) and "不停" (bùtíng). Instead of usually being adjectives, these two words are usually adverbs (but they can sometimes be adjectives too!). However, they are used in different ways and different places, so this article will help you distinguish when and where to use them.

不断

"不断" is usually placed before the verb it modifies, and it often requires the particle "地" to show that it is an adverb.
Subject + 不断 + 地 + Verb

Examples

Kèhù búduàndì ɡǎibiàn zhǔyi, zěnme bàn?
客户 不断地 改变 主意,怎么 办?
The client won't stop changing his ideas. What should I do?

Guòqù de liǎnɡ nián lǐ, wǒmen búduàndì zài nǔlì, yě búduàndì zài jìnbù.
过去 的 两 年 里,我们 不断地 在 努力,也 不断地 在 进步。
For two years, we continuously pushed ourselves and continuously improved.

Tāmen zhījiān de máodùn yìzhí búduàn, ɡuānxi búduàn èhuà.
他们 之间 的 矛盾 一直 不断,关系 不断 恶化。
The argument between them is ongoing. The relationship is consistently worsening.

不停

"不停" is a little more versatile and can be placed both before the verb as an adverb, or after the verb as something that is somewhat like a complement. Either way, it means the same thing.
Subject + 不停 + 地 + Verb

Examples

Wǒjīntiānhěnkùn, bùtínɡdìdǎhāqiɑn.
我今天很困,不停地打哈欠。
I'm so tired today. I can't stop yawning.

Gǎnmàole, hóulónɡtònɡ, háibùtínɡdì liúbíshuǐ.
感冒了,喉咙痛,还不停地留鼻水。
I got a cold. My throat hurts and my nose keeps running.

Chīfàndeshíhou tāyíjùhuà yěbùshuō, bùtínɡdìchī.
吃饭的时候他一句话也不说,不停地吃。
When he's eating, he doesn't say anything. He doesn't stop eating.

When "不停" comes after the verb, it behaves somewhat strangely and takes "个" before it in order to become grammatical, like so:
Subject + Verb + 个 + 不停

Examples

Háizi kū ɡèbùtínɡ, shì bú shì fāshāo le?
孩子 哭 个不停,是 不 是 发烧 了?
The child is crying constantly. Does he have a fever?

Jīntiān diànhuà xiǎnɡɡèbùtínɡ, fán sǐ le.
今天 电话 响个不停,烦 死 了。
The phone is ringing incessantly today, it's so annoying.

Yìtiāndàowǎn lǎopo láodāo ɡèbùtínɡ, nǐ shòu dé le mɑ?
一天到晚 老婆 唠叨 个不停,你 受 得 了 吗?
In the evening, the wife doesn't stop chatting. Can you stand it?