a serious/minor offence
重/轻罪
a criminal/drink-driving offence
刑事罪/酒后驾车罪
Driving without a licence is an offence.
无照驾驶是违法行为。
He committed several serious offences.
他犯了好几项重罪。
It's the third time that he's been convicted of a drug offence.
这是他第三次因毒品犯罪被判刑。