alternate(ly) and alternative(ly)

Alternate(ly) means ‘first one and then the other’, ‘in turns’.

• We spend alternate weekends at our country cottage.
• I’m alternately happy and depressed.

Alternative(ly) is similar to ‘different’, ‘instead’, ‘on the other hand’.

• Jessica’s not free on the 27th. We’ll have to find an alternative date.
• You could go by air, or alternatively you could drive there.

In American English, alternate(ly) can be used with the same meaning as alternative(ly).