It was sunny in Moscow on Jan. 31, with temperatures around minus 14 degree Celsius/7 degrees Fahrenheit, but despite the cold, the city saw a number of anti-government rallies – and some fighting. Below are a few accounts, some photos, videos, and links.
LJ user drugoi posted nine photos from the opposition rally on Bolshaya Polyanka  and wrote this (RUS):
Young opposition activists have once again succeeded in marching down a Moscow street today. This time it was Bolshaya Polyanka, and the participants of the rally […] were getting there in roundabout ways, switching trains on the metro. Today, however, it turned out that the regime had some volunteer (or, perhaps, hired) assistants. […]
The moment the column of approximately 50 to 80 “dissenters” with flags and banners started moving along Polyanka, a few cars drove up from behind and – with the words, “Why aren't you letting us relax, assholes?” – some 10 or 12 people got out, dressed uniformly: in jogging pants, jeans and hooded jackets. Without delay, the gang started beating the protesters, and a pretty serious fight began.
There was some initial confusion in the “dissenters”‘ ranks, but then they were quite organized and tough as they fought the attackers back. Among the protesters, there were people with blood on their faces, one of the reporters had a stone thrown at his camera, but the attackers were forced to run away and would have been chased if the opposition activists hadn't decided to continue on their march.
At the end of the fight, those who were covering their faces with scarves sprayed some tear gas around. Many of those who were affected had to wash their eyes.
Riot police showed up only after the rally was over, and the work of all the law enforcement organs had to be done by two police [officers] from a nearby station, under the sharp eye of a dark-blue police helicopter hanging over Polyanka.
Several times they jumped bravely into the protesters’ crowd, trying to take the banners away. It was causing some serious resistance, but the protesters had more people and [the police officers] obviously didn't have the guts to face up to them.
Desperate, one of the policemen rushed to a group of soldiers he saw standing on the sidewalk, and begged them to join in the difficult task of protecting public order. The cadets reluctantly shifted from one foot to the other, but didn't go against the people's will.
All in all, the Dissenters’ March has again taken place, and there was more than enough drive today. Riot police units, which showed up belatedly […], seized whoever was within reach – a cameraman, for example, with a huge Betacam on his shoulder – placed them into the [police van] and drove away. Somewhere above the square a new police helicopter hung still – all it had left to do was register the fact that the “dissenters” have managed to achieve what they wanted today.
LJ user zyalt posted nearly 30 photos from the same rally  in the oppositional namarsh_ru LJ community.
Russian photographer Oleg Klimov posted a few pictures of the National Bolshevik leader Eduard Limonov , who made an attempt to hold another rally on Jan. 31 – a follow-up to the protest by the Communist Party at Triumphalnaya Square. Here're some of Klimov's observations (RUS):
[…] Triumphalnaya Square, in front of the monument to [poet Vladimir Mayakovsky], was cordoned off by riot police – and empty. There was a crowd by the entrance to the metro, though, not allowed to come to the stone “revolutionary poet” – and the loudspeaker kept addressing them loudly: “The rally is over! Go home!” Most of these people were journalists and they didn't want to disperse. They were waiting. Waiting despite the fact that the [National Bolshevik activists] and other young people had already been arrested and squeezed into [police vehicles].
We walked out [from the opposite side of the square] and it seemed as if nobody noticed us. Limonov started his speech by the monument to Mayakovsky. The crowd by the metro got somewhat excited, but riot police were holding them tough. Some of the journalists managed to break through, however, and ran towards Limonov. Riot police ran after them. Things were happening around the revolutionary writer [Limonov] as well. He continued talking, most likely about “freedom, fraternity and equality,” surrounded by his personal guards, but at some point two huge plainclothes guys pushed over simultaneously on Limonov's bodyguards and hit one of them right into his nose. It was just an ordinary fight. Limonov was thrown on the asphalt, but, as an experienced revolutionary, he managed to take his glasses off, to keep them from being broken, obviously. The guards did their best to protect him, but the riot police were there soon, and it all ended the way it always does – the doors of the [police vehicle] […] were shut close.
The crowd was just staring at what was going on – with obvious pleasure, it seemed. No one said anything. No one yelled anything. No one cursed anyone… the crowd was observing, along with the journalists. Observing lawlessness and impunity of the “cats” who didn't like one “little mouse” that was not gray.
There was a feeling of sadness because of this, and a terrible embarrassment, because, as Johann Goethe, I guess, said – “None are more hopelessly enslaved than those who falsely believe they are free.”
Below is a video of the events at Triumphalnaya Square, posted  by LJ user zlaya-uchilka:
According to LJ user alaverin  (RUS), Eduard Limonov is to spend the night and part of Feb. 1 at the police department.
A pro-Kremlin rally took place just off Red Square on Jan. 31, too. LJ user drugoi posted a photo  of one of the banners from that event: “We believe!” – underneath the portraits of Dmitry Medvedev and Vladimir Putin. Some of drugoi‘s readers thought the banner looked familiar, in two different ways:
I thought at first that this was an Obama poster.
Long live CPSU.
How deep must the USSR still be in the people that even after nearly 20 years the same style of banner design comes up.
It never went away anywhere, they've just done a little re-branding, Putin instead of Lenin, [Medvedev] instead of Stalin, and the CPSU has renamed itself into [the United Russia party].
LJ user mutin2007 posted a sheep cartoon , on which the animals hold banners thanking the regime for price hikes and layoffs, among other things.
Also, LJ user mutin2007 posted a photo  from a rally that took place on the same day all the way across Russia, in Vladivostok: a group of protesters there carried a banner with the words “Putler kaput!!!” on it.
LJ user bwm posted 16 more photos from the Vladivostok rally , organized by the Communist Party and the Community of Activist Citizens of Russia (TIGR), and wrote this (RUS):
[…] The march turned out to be pretty strange because [TIGR activists] didn't really have anything in common with the Communists – neither in their appearance, nor in their [political views].
But most of the protesters were people who did not belong to any political movements, but were just not indifferent to the realities around them. […]