The latest march, in central Istanbul, was one of the demonstrations prompted by the recent murder of a 20-year-old Turkish woman.
Ozgecan Aslan, a university student, was killed in an attempted rape.
"The way of thinking that 'a woman wearing a miniskirt deserves rape' is sick," said Ali Erkazan, who represented the men wearing the skirts.
"We demand, as democratic and intellectual men of this country, freedom for women, free expression, opportunities for women, and equal rights for women as for men."
Men and women marched through the streets carrying photographs of Aslan, whose body was found on 13 February in a riverbed in the southern province of Mersin.
She had last been seen two days earlier on a minibus, the driver of which has since confessed to killing her and mutilating her body, Turkish media reports.
He was arrested along with his father and one other man.
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It puts new, lower limits on the size of each country's nuclear arsenal, and updates the verification mechanism.
There are limits on warheads and on launchers, which must be implemented within seven years of the treaty's entry into force.
Warheads: Under the New Start treaty each side is allowed a maximum of 1,550 warheads. This is about 30% lower than the figure of 2,200 that each side was meant to reach by 2012 under the Start treaty (as revised in the 2002 Strategic Offensive Reductions Treaty).
Launchers: Each country is allowed, in total, no more than 700 deployed intercontinental ballistic missiles, submarine-launched ballistic missiles, and heavy bombers equipped for nuclear arms. Another 100 are allowed if they are not operationally deployed - for example, missiles removed from a sub undergoing a long-term overhaul.
The new limit on delivery systems is less than half the ceiling of 1,600 specified in the original Start treaty.
Not as dramatic as they might appear. The rules for counting warheads contain a big loophole. While each warhead on a ballistic missile is counted as one warhead, a heavy bomber is counted as carrying "one warhead" even though it may carry (in the case of a US B-52) up to 20 of them.
According to the Arms Control Association, a pro-disarmament pressure group, the US could theoretically meet the new limits by cutting just 100 warheads, while Russia would only need to cut 190.
In addition, the agreed ceilings refer to deployed warheads, not to warheads in storage. A warhead could, in theory, be put into storage, and then redeployed when needed.
The cuts in launchers are also, in practice, not all that challenging. The Bulletin of the Atomic Scientists estimates that Russia currently has 566 - well under the permitted ceiling of 700. It estimates that the US has 798, necessitating a cut of about 12%.
Supporters of the deal say that while it does not make big cuts, it is a useful confidence-building measure, which could pave the way for further nuclear deals with Russia.
They say it also signals to the rest of the world that the US and Russia are not ignoring their commitment under the nuclear Non-Proliferation Treaty to progressively disarm.
The important difference, according to the Arms Control Association, is that each side will now be able to carry out on-site inspections to verify how many warheads a missile is carrying. Together with satellite imagery, this should give an accurate picture of the other country's nuclear strength. Some other forms of verification will cease.
Yes, it says that both sides can engage in "limited" missile defence. Russia has warned that it will withdraw from the treaty if a future US missile defence shield weakens its nuclear deterrent.
The US Senate ratified it on 22 December, after much delay, so now all it needs is Russia's final approval. Russia's parliament, the Duma, is expected to ratify it - and the process may begin on 24 December.
The US wants further cuts in strategic nuclear arms, but is also keen to negotiate a reduction in Russia's short-range nuclear missile arsenal.
Russia wants the US to remove its 200 nuclear bombs from Europe (based in Germany, the Netherlands, Belgium and Turkey) and would like to restrict the US's ability to put conventional warheads on long-range missiles.
Groups of men in Turkey are wearing skirts to protest against violence towards women.
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The New Start treaty, signed by the US and Russian presidents, replaces the Strategic Arms Reduction Treaty (Start), first proposed by US President Ronald Reagan in 1982 and signed in 1991, as the USSR sped towards collapse.