Police investigating the case said they believed the family of the woman, aged around 20, was responsible for the murders in the southern province of Helmand, a lawless hotbed of the Taliban insurgency.[break]
The elder brother of the male victim, who was in his 20s, told officers the woman had run away with him recently and was living in their family home.
On Monday, 10 men broke into the house near the provincial capital Lashkar Gah and kidnapped the pair, police official Mohammad Ismail Hotak told AFP.
"On Tuesday, local residents reported that there were two bodies in the graveyard. We went there and found them. Both were beheaded," he said.
"From our investigations, we have found that the two had a love affair. We believe the family and relatives of the girl are behind the killing."
The police official said the brother told investigators the dead man had loved the woman and wanted to marry her.
Omar Zwak, the provincial governor´s spokesman, confirmed the incident and said an investigation was under way.
Relations between young men and women outside marriage are taboo in Afghanistan, an extremely conservative nation with deep Islamic beliefs.
Most marriages are arranged by family elders, in some cases without the couples being consulted.
A man attempting to establish relations with a woman is seen as an insult to her family´s honour and often leads to violent revenge.
In such cases, the woman is often also killed for supposedly bringing shame to the family.
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