You can claim zero dependents if you work two jobs - that means your employers will withhold the maximum amount possible for your taxes. This is a good idea, because when you add the two jobs together, your tax bill can be greater than the amount of withholding, and then you will owe the IRS and possibly your state.
If by "0 and 0" you mean "Exempt for both" this is not a good idea. If you don't have any withholding, you could end up owing the IRS and/or your state, PLUS having to pay penalties and interest.