The scandal comes on the heels of weekend local elections won by the Social Democrats, followed by the Respublika and Fatherland (Ata Meken) parties.
There have already been allegations of fraud in the November 25 vote, including by the leader of the coalition Dignity (Ar-Namys) party, Feliks Kulov, who quit his coalition post in protest.
In the "carousel voting" scheme outlined in the videos, people submit ballots at a number of different polling stations. Since Kyrgyzstan's own Tulip Revolution erupted over flawed elections in 2005, the practice has marred elections in Kazakhstan and Russia and been alleged elsewhere.
The videos in question show Respublika candidate Nargiza Azhybaeva (the woman in glasses) on two separate occasions seemingly coaching listeners on techniques that enable people to vote multiple times.
She tells them to "make sure your thumb is cleaned," to erase the permanent ink, and avoid parking together -- at least "a 100-meter interval from each other." She also tells them to approach "the woman in the middle of the table with a big scarf around her and tell her our code words: 'When will the district polling [station] be closed?'" She advises them to use some Kyrgyz and some Russian language and to be quiet and "don't provoke any suspicion."
"If somebody notices your passport is different," she says at one point, "just leave quickly, apologize, [and] say that you made a mistake. Make up some last name starting with M or N."
Noting that there are police and security officers at polling stations, in addition to people from other political parties, she says, "Don't laugh when you leave the polling station; be serious and quiet."
You can see the videos here and here.
The 27-year-old Azhybaeva is something of a rising star in her party, busily promoting herself on social networks, including in photos showing her with Respublika leader and former Prime Minister Omurbek Babanov.
She was 21st on Respublika's candidate list for the Bishkek City Council in the November 25 elections.
The Respublika party has expressed outrage at what it says is "a provocation prepared by Kyrgyzstan's secret services." Respublika Chairman Babanov was prime minister from December 2011 to September of this year.
The videos in question sparked particular interest from authorities after gaining widespread attention one day after the voting.
RFE/RL's Kyrgyz Service says Azhybaeva reappeared in a Kyrgyz television interview on November 28, citing a murky encounter with local security services in 2010 but shedding little light on the allegations or her actions in the video.
Her comments -- and indeed the entire scandal -- appear to have been greeted with widespread skepticism in Kyrgyzstan, where street protests have already unseated two presidents in the past seven years.
-- RFE/RL's Kyrgyz Service