If I start a new company and I have an existing company, can my new company be liable for old companies debts?

Possibly, especially in New Jersey. First of all, I assume that the companies are both legal entities,such as corporations or llc's, or the question wouldn't even arise. Second, if the second company acquires the assets of the first, and the first is unable to pay its obligations (i.e. the money it owes the client), the transfer of assets would be a fraudulent conveyance unless the second company paid the first fair consideration for the assets.  In other words, if the assets are worth $30,000, and the second company only pays $500 for them, that is likely to be considered a fraudulent conveyance to the tune of $29,500, for which the second company could be liable.  The second company could avoid that threat by paying fair value (although there can always be disputes over what consitutes fair value), but if the 2nd company pays the first $30,000, the first will have to pay the client with that money, so I don't see how you'd be better off.  Third, even forgetting any fraudulent conveyance issue, if the new company continues to conduct the same business as the first it could be deemed to be a successor to the first, especially if it is owned by the same people, operates out of the same space, has the same employees, etc.  If deemed a successor, the second company would be responsible for the first company's obligations.  New Jersey law is fairly strict on the issue of successor liability (stricter than NY, for example.)