What is the right format of a second use claim? Is it the same as the swiss style format? The patent office in my country does not accept the swiss style claims that I submitted, then I am supposed to change them into second use claims.
The phrase "second use claim" and the swiss style format allow me to assume you are Europe-based.
You don't mention if it is a second medical use claim or not. If it is a second medical use claim, the (new) style accepted at the EPO is demonstrated in the Guidelines: http://www.epo.org/law-practice/legal-texts/html/guidelines/e/g_vi_7_1.htm and boils down to the following format: "Product X for use as a medicament".
It can get even more specific. So if X is known generally as a medicament, but not e.g. for cancer, you can still get a claim like "Product X for use in the treatment of cancer" if it is novel & inventive.
If it is a non medical use, it might be more difficult to get a patent for it or even phrase it in a way that has decent chances of leading to grant. This is because prior art usually discloses something in a form that inherently comprises the use you are trying to claim.
In my field (organic chemistry), it is not that unusual to claim something like "Use of compound X as an intermediate in the synthesis of...". It is not very easy to get such claims, because it is hard to get an inventive step, but depeneds on the case.
For simple use claims, every case is different. Take a look here for that matter: http://www.epo.org/law-practice/legal-texts/html/caselaw/2016/e/clr_i_c_8_1.htm
and here for the claim style: http://www.epo.org/law-practice/legal-texts/html/guidelines/e/g_vi_7_2.htm