For Germany, the new German state assumed the responsibility for the approximately $20-6 billion of foreign debt incurred by the GDR. Article 24 (1) of the Reunification Treaty stated:

In so far as they arise from the monopoly on foreign trade and foreign currency or from the performance of other state tasks of the German Democratic Republic vis-à-vis foreign countries and the Federal Republic of Germany up to 1 July 1990, the settlement of the claims and liabilities remaining when the accession takes effect shall take place under instructions from, and under the supervision of, the Federal Minister of Finance. Debt rescheduling agreements contracted by the Government of the Federal Republic of Germany after the accession takes effect shall also incorporate the claims mentioned in the first sentence. The claims concerned shall be held in trust by the Federal Minister of Finance or transferred to the Federation to the extent that the claims are adjusted.

Although the new German government took responsibility for these debts, there were some qualifications involved in the Treaty. Article 24 (3) contended that the GDR's debts incurred with the now defunct COMECON members were a special case and would subject to separate negotiations with the unified Germany. The rationale behind this was that the economic relations between the Warsaw Pact states were not conducted in a free-market environment and therefore subject to renegotiation. Both the UN and the World Health Organization sought to have Germany assume the responsibilities for the GDR's pledged and overdue financial obligations to these international groups in addition to the FRG's own responsibilities. The Kohl government voluntarily paid for these obligations, but noted that they were ex gratia and not because Germany felt obligated to do so.

Although the GDR's foreign debt was a burden for the newly unified state, the costs of assuming control and privatizing the GDR's vast network of outdated state-controlled industries was an even greater task.

Regarding USSR, Russia took on itself all properties and debt of USSR. According to news reports such as this and this, by 2006 all USSR debt was paid by the Russian Federation, even ahead of the schedule.

The nature of the debt, its repayment, possible debt forgiveness and restructuring and the role of the so called Paris club of creditors is something that I unfortunately do not know much about

---

What I might expand a bit, is the interesting case of USSR debt to Yugoslavia. ( It enters 20 years rule, but as a consequence of previous events, it might be tolerated? ) As both USSR and Yugoslavia dissolved, the situation of the debt became complicated.

While Russia took on the USSR debt, it wasn't until 2001 and the signing of the Agreement on succession of Yugoslavia that the ex-Yugoslav nation finalized the division of property of Yugoslavia state between themselves. The agreement (link in Croatian) can be found here

If anyone is interested the property (embassies, property and money in local and foreign banks) was divided by something along the lines of the following percentages:

country	percentage
Bosnia & Herzegovina	13,20%
Croatia	28,49%
Macedonia	5,40%
Slovenia	16,39%
FR Yugoslavia*	36,52%

*Serbia and Montenegro

After that point (2003) Russia and ex-Yugoslav nations had meetings to agree on their debt. The amount agreed to was 1.2 billion USD that USSR owned to Yugoslavia and would repay to ex-Yugolsav countries in the form of clearing agreement. Each ex-Yugolsav country would inherit the percentage of the debt according to the above percentage.
Then Russian Federation had negotiations with each country individually in to how this debt would be repaid. As it was that from of clearing agreement, it would be paid in form of materials and services. For example of Croatia, the only one I know, the debt inherited was 28% totalling 185,7 million USD. In 2006 the agreement was made that the debt would be repaid in equipment for thermal power plant in Sisak (105 mil), building a gas pipeline (15.7 mil) and acquiring 10 transport helicopters for military and rescue (65 mil)
By end of 2011 the debt was repaid in full