How to express vague amounts of time?

I'm having trouble figuring out how to express vague amounts of time in Japanese, such as some number of months or some number of hours.

I want to use this in a context where the specific number is neither important nor known, but the factor of time passing/occurring is important. For example:

Some hours later, he finished the test.

Traveling to and staying in another country requires some number of months free.

Answer

Two constructions spring to mind here.

数{すう} can be used in place of a specific number, followed by a counter, to mean "some" / "a few" / "several" (it doesn't really make a distinction in this respect...).

数時間後、彼は試験を終わった。

This can be used in ways you might not expect:

数十秒 some tens of seconds
十数秒 ten-(and-some)-odd seconds (between 10 and 19)
二十数年 twenty-(and-some)-odd years

Alternatively, you can use 何 + counter + か.

他の国に滞在するなら、[何ヶ月]{なんかげつ}かは開いておかなければなりません。

The same kind of uses seen above for 数 also apply to 何.