Alekseev has led efforts to openly celebrate LGBT Pride in Moscow since 2005. Each year Moscow Mayor Yuri Luzhkov has banned it, but Alekseev and a small band of activists have defied officials, often ending up detained or arrested by police and, at times, attacked by counter-protesters spurred on by anti-gay Russian Orthodox clerics and the homophobic hate speech of Luzhkov himself.
"They (Moscow officials) couldn't imagine that there was someone who would fight this, who would come back and do this again in 2007, 2008, 2009," Alekseev said. "They couldn't imagine that in just three years after Moscow Pride started that the international reputation of the mayor was ruined."
Luzhkov was finally sacked as mayor by higher-ups in the government last fall, something the LGBT activists take major credit for, Alekseev said. Time and again the activists exposed Luzhkov as a blatant and extreme homophobe, to the point that foreign dignitaries no longer wanted to meet with him publicly.
"We made a big contribution to ruining his political career," Alekseev said.
Not only have Alekseev and the LGBT activists fought the government by defying the bans on Pride year after year, they've fought them in the courts, both in the Russian courts and in the European Court of Human Rights.
In Russia, that hasn't gotten them far, Alekseev said.
"In the Russian courts we lost everything, every case," he said. The courts are totally controlled by the government. There are no more free elections. The media is largely controlled by the government, especially TV."
But in the European Court of Human Rights it's been a different story. There, last October, Alekseev won a major victory over the Russian government when the court ruled that the government had "failed to demonstrate any pressing social need" to ban Moscow Pride and ordered the government to allow the marches on the grounds of people's right to free assembly.
"It was unanimous," Alekseev said. "Even the Russian judge voted in our favor."
The Russian government has appealed but has little chance of winning.
"They have no chance of winning this," Alekseev said. "They know that they are going to lose. They know this very well."
The appeal was made, he added, "probably under the pressure of the Russian Orthodox Church."
The Russian activists expect the ruling in early May, just before their annual May 28 Moscow Pride celebration. Alekseev said the Russian government could decide to not honor the ruling and move to stop the Pride event again.
"If they don't, we will of course go on the street anyway," he said.
Whether the government respects the European Court ruling or not, losing it was a huge embarrassment to them. It gives foreign diplomats and others an opportunity to raise official concerns about how LGBTs are treated in Russia, Alekseev said, and exposes the government's official denials about the issue.
"It was a major blow for the Russian government because it was the first-ever defeat at the European Court of Human Rights for the Russian government," Alekseev said. "And it shows there are violations of the rights of LGBT people, which is contrary to what the government always claimed."
He said it's not just a win for LGBT activists in Russia, but also for other groups there that have been denied the right to assemble, protest and advocate for their issues.
"It's the first-ever verdict on freedom of assembly in Russia," Alekseev said. "It surprises me that gays were the ones who won the first case because we started our movement only in 2005."
An attorney, Alekseev has other cases pending at the European Court, including ones dealing with the right of free association and with Russia's laws excluding gays and lesbians from marriage.
"It's an investment in the future," he said. "Maybe we will not in five years earn the right of marriage but I'm absolutely assured we will win something similar to it. You will see that in five or six years we will have a national debate on the rights of lesbian and gay families."
International pressure has helped, Alekseev said. When he and the activists called their first press conference, no journalists showed up. But support from the international community has helped, including visits by foreign politicians and activists such as London's Peter Tatchell and Chicago's Andy Thayer to take part in Moscow Pride. That's raised the visibility of the struggle for LGBT rights there - the media responds and the government, Alekseev emphasized, has noticed.
"There are lots of ways that you can, for example, help," he said. "Take a stamp and send a letter signed by many people to the Moscow authorities. They will see it. You can always write to your congressmen asking them to raise this problem. This will be very effective."
Alekseev showed a short video of scenes from previous Moscow Pride events, many including footage of police harassing and arresting Pride marchers. Following his talk, he answered questions from the audience. His appearance in Chicago was sponsored by the Gay Liberation Network.
"The purpose of the tour, starting here in Chicago...is to basically raise awareness in the United States so that when and if the Russian government decides to ignore the ruling May 28 there will be a howl of protest here," said GLN's Thayer.