After a 5-hour trial, a court in Ho Chi Minh City sentenced Tran Vu Anh Binh, 37, to six years in jail and Vo Minh Tri, 34, was handed a 4-year prison sentence, the BBC reported. Both were arrested late last year.
A particular area that concerned the court was the musicians' criticism of China's claim to island territories in the South China Sea and the Hanoi government's response to the claims, the BBC said.
Vietnam and China have fought brief but pitched sea battles over the mostly unoccupied Spratly and Paracel islands in the past 30 years.
Human rights groups criticized Vietnamese authorities for putting the singers on trial and called for their release.
"This is a ludicrous way to treat people just for writing songs," Rupert Abbott, Amnesty International's researcher on Viet Nam said just before the trial.
"These men are prisoners of conscience, detained solely for the peaceful exercise of their right to freedom of expression through their songs and non-violent activities and should be freed," Abbott said.
"There is a very disturbing trend of repression against those who peacefully voice opinions the Vietnamese authorities don't like."
Amnesty International also called for the release of 20-year-old university student Nguyen Phuong Uyen, one of four people arrested earlier this month for allegedly distributing anti-government leaflets.
She reportedly criticized China and the Vietnamese authorities, Amnesty International said on its website.
Last month Vietnam was rebuked by many countries, including the United States, for sentencing three bloggers for carrying out "propaganda against the Socialist Republic of Vietnam."
"Just as in other countries, all law violations are punished in accordance with regulations of Vietnam's law and international human rights law, including the International Covenant on Civil and Political Rights," a Foreign Ministry spokesman said at the time.
Nguyen Van Hai, known as Dieu Cay, 60, was sentenced to 12 years in prison on a charge of spreading propaganda against the state. Ta Phong Tan, 44, received a 10-year sentence and Phan Thanh Hai, 43 and a lawyer, was ordered to three years in jail.
All were members of the Free Journalists Club, an independent bloggers' website, and were thought to have posted more than 400 articles, including 26 items containing anti-state comments.
Cay, a former soldier and a founder of the Free Journalists Club, was mentioned by U.S. President Barack Obama in his statement on World Press Freedom Day in May.
The recent sentences continue the regime's crack down on public displays of anger against the government's perceived corruption and mismanagement of the economy, the BBC reported.
Earlier this month, Communist Party chief Nguyen Phu Trong publicly apologized for the behavior of some government officials for their accumulation of wealth while many Vietnamese struggle.
Prime Minister Nguyen Tan Dung is under pressure not just from outside critics but also from those within the Communist Party who want major changes and are fighting for control.
Dung also apologized during the opening session of Vietnam's National Assembly this month, saying his government's policies had led to large losses at banks and the collapse of state-run companies including shipbuilder Vinashin.
He also lowered the government's 2012 economic growth target to 5.2 percent from a previous range of up to 5.7 percent -- the slowest growth since 1999 and down from 5.9 percent in 2011, the Financial Times reported.
"I personally apologize to the National Assembly, to the party and to the nation for the government's weakness in economic management, especially in the supervision of the operation of state-owned groups and companies, such as shipbuilder Vinashin and shipping firm VinaLines," Nguyen said.
After a 4-day trial in April, a Vietnamese court in Haiphong sentenced Pham Thanh Binh, the former chief executive of Vinashin, to 20 years in prison, The Wall Street Journal reported.
He was convicted of ignoring government regulations for running state-owned businesses and taking the firm known formally as Vietnam Shipbuilding Industry Group to edge of bankruptcy.
Seven other executives received sentences of 10-19 years in prison on the same charge, while another received a 3-year sentence for misusing government property, the Journal reported.
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