But they came to a peak this week when Russian-speaking militia closed a school for orphans, forcing the children to stay with teachers.
The children later barricaded themselves inside in protest. Parents and teachers were arrested at another school as they staged a sit-in to prevent its closure.
The closures prompted a harsh response from Moldova's government.
On 29 July, they announced sanctions on Transdniester, in effect barring the export of goods from the region.
President Vladimir Voronin told lawmakers this week that his government no longer accepts Transdniester's authorities -- led by Igor Smirnov -- as equal partners in political negotiations.
"Today Smirnov has taken children hostage only because they learn the Moldovan [Romanian] language based on the Latin alphabet. Tomorrow, to save the ideological base of his regime, he will start [blackmailing] us with the revival of the conflict. Already Smirnov and his circle are no longer separatists who defend their political rights or autonomy of the Transdniester region," Voronin said. "They are only shabby fellows who do not deserve any other name. This is an international criminal group and that's why we do not accept any longer the current [Transdniestrian] administration as equal part in the negotiations for the political solution to the situation. As long as the people from Transdniester will not have access to real democratic mechanisms we will not launch any positive initiative."
Transdniester's authorities say they have earmarked seven schools for closure because they teach Romanian/Moldovan using the Latin alphabet and not Cyrillic. That alphabet is predominantly used in Transdniester, as during Soviet rule.
But the closures have drawn international criticism.
The European Union on 28 July threatened to take action against Transdniester unless authorities resolve the dispute.
And the Organization for Security and Cooperation in Europe (OSCE), which monitors human rights, has called the closures "linguistic cleansing."
"The situation in all of the places is very tense and according to us it is quite explosive," said William Hill, the head of the OSCE mission in Chisinau. "I personally have visited one of the boarding-schools where the situation was quiet but pretty tense. The situation in all of the three of the places is unpredictable, both for the presence of authorities and for the threats of the closed schools."
Today, the president of Romania, whose territory once included most of Moldova, expressed his concern. Ion Iliescu said he had appealed to Russia to intervene in the crisis because Moscow has influence over Transdniester's separatist leaders.
"We follow with great concern what is going on in Transdniester. I wanted to make a statement on this matter regarding this savagely primitive manifestation for the beginning of the 21st century, this manifestation of an attitude that is totally against the spirit of the times," Iliescu said.
The school dispute is the latest flare-up of a row that goes back more than a decade.
Transdniester broke away from Moldova in 1990 and the two sides fought a short war in 1992. But the region has no international recognition and efforts to resolve the dispute so far have failed.
And Russian troops, which quelled the 1992 war, remain there despite Moscow's promise five years ago to remove them.
As this latest dispute escalates, teachers and parents at the schools are calling on all parties to think of the ones being most affected -- the children.
A professor at one of the schools in Ribnita read an open letter appealing to the Chisinau parliament and to the wider public: "The situation now puts under danger the fate of 620 Moldovan children. It's a big danger. The reconstruction works were financed by the Republic of Moldova. We count on your generous hearts and we wait for a decision on which depends the future of our children and of our country."
(This story was compiled from reports by Ileana Breitenstein and Oana Serafim of RFE/RL's Romanian/Moldovan Service and news agencies.)