The court said on its website that the rulings were made on September 4, but that they had only been made public on Thursday.
The plaintiffs had repeatedly appealed to the Russian courts before eventually taking their cases to Strasbourg.
The parents of Adnan Akhmadov accused the Russian authorities of being involved in the disappearance of their son in September 2002. They say Russian servicemen detained Akhmadov, something witnesses have confirmed, and insist that law enforcement agencies did not thoroughly investigate the case.
Russia denied that its servicemen were involved in the incident, and said that Akhmadov was abducted by unknown armed people.
In the second case, Ruslan Medzhidov accused the Russian authorities of being guilty of the death of his parents, brother and two sisters when Russian forces shelled their village in 1999. Russia has denied that its forces were responsible for the shelling of the village.
Chechnya suffered two devastating separatist wars in the 1990s-early 2000s. Thousands were killed and many more made homeless as federal troops attempted to regain control of the mountainous republic.
Earlier this year, the Council of Europe harshly criticized Russia over alleged human rights violations by security forces in Chechnya and other parts of Russia's North Caucasus, including torture and executions.
In total, the European Court of Human Rights has received a total of 46,700 cases against Russia over the past ten years, comprising 20% of all lawsuits submitted.
The court has made about 400 rulings on Russia in the past 10 years, or 5% of the total received during the period.