Two members of the anti-Putin activist group Pussy Riot have vanished in the annexed Crimean Peninsula, their worried bandmates have revealed.

Olga Borisova and Sasha Sofeyev had been detained multiple times by Russian secret police in the disputed territory claimed by both Russia and Ukraine before they disappeared.

The women were due to fly from Simferopol to Moscow on Monday night, but failed to board the plane and their friends have been unable to contact them.

Their whereabouts remain a mystery as Pussy Riot, a feminist protest musical group whose outspoken members have had several run-ins with Russian authorities, desperately try to find out what happened to them.

After they vanished, leading Pussy Riot member Maria Alyokhina was attacked and detained in Crimea on Tuesday for the second time in two days, the band claimed.

The group appealed for information on Twitter, saying the women had previously been detained by the the Federal Security Service (FSB), a successor to the KGB.

The group wrote: "Two Pussy Riot members are missing. Olga Borisova & Sasha Sofeev disappeared in Crimea yesterday.

"FSB detained them several times. Yesterday cops broke their phones and computers.

"We can not reach out to them.

"We don't know what has happened to them."

Pussy Riot member Nadezhda Tolokonnikova, 28, who was jailed in 2012 for hooliganism after performing in a Moscow church, wrote on Facebook: "My closest friends and members of Pussy Riot Sasha Sofeyev and Olya Borisova disappeared in the Crimea."

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She claimed police officers in Simferopol had smashed their phones and confiscated other electronic equipment.

Ms Tolokonnikova added: "From approximately six o'clock in the evening yesterday Olya and Sasha have not contacted anyone. They were not on any of the planes that flew in to Moscow yesterday evening."

She claimed Ms Alyokhina - who was also jailed for the church performance in which the group sang a "punk prayer" against Vladimir Putin - was attacked with whips and detained by police in Simferopol where she planned to take part in a protest in support of Ukrainian filmmaker and writer Oleg Sentsov.

Mr Sentsov was arrested in Crimea on accusations of plotting terror attacks and jailed for 20 years by a Russian court. However his supporters say the claims against him were fabricated.

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Ms Alyokhina was arrested on Tuesday at a cafe after she was confronted by men in traditional Cossack military uniforms, who called themselves members of "Crimea's self-defence", Radio Free Europe reported.

She and Ms Borisova and Ms Sofeyev were detained in different parts of Simferopol on Monday and taken to a local medical office for tests, although it was not clear why the tests were carried out, the report added.

They were later released.

Ms Borisova and Ms Sofeyev had decided to return to Moscow after they were detained several times by security officials during their visit to Crimea, Ms Alekhina had told the website Media Zone.

They had agreed to call Ms Alyokhina from a new or borrowed phone at the airport, but the call never came, the report added.

A taxi had taken the missing women to the airport in Simferopol at about 8pm local time, and the pair had planned to buy their tickets there.

The last flight to Moscow departed just before 9pm.

They didn't arrive in the Russian capital and they were not found at the Simferopol hotel where they had been staying, Media Zone reported.

The woman didn't arrive on any flights on Tuesday morning.

In August last year, Ms Alyokhina and Ms Borisova were arrested and later fined after holding a protest near the Siberian prison where Mr Sentsov is being held.