Washington ? “Authoritarianism in the name of Islam is dead,” messaged one Egyptian activist last Sunday, as millions gathered to denounce the rule of President Mohamed Morsi and his Muslim Brotherhood government.

There’s a new wave of popular dissent this July 4 in Egypt, Iran and Turkey, the region’s three biggest Muslim democracies. Authoritarianism is still very much alive in the Middle East, but it’s under pressure from a surprisingly broad movement for change that defies religious or nationalist sloganeering.

The faces and styles of protest are different as you move across the map, but the basic message is the same: We are citizens. We want dignity and human rights. We aren’t afraid of autocratic leaders or their secret police.

That’s how this movement began, with a defiant street vendor in Tunisia in late 2010, and it’s still echoing.

“It’s a second revolution,” Ahmed Said, a leader of Egypt’s National Salvation Front, told the Guardian newspaper.  At this writing, it’s unclear how the mass protests will end — but Morsi’s attempt to impose Muslim Brotherhood policies on a diverse Egypt have failed. The Egyptian army — the only institution in the country with broad support — now holds the balance of power.

What’s fascinating is that the new challenge to religious parties in the Middle East transcends sectarian lines. The protest against the Muslim Brotherhood in Sunni Egypt is matched by a similar renewal of dissent in Shiite Iran, where the 2009 Green Revolution was crushed by government repression.

The unlikely emblem of change in Iran is Hassan Rouhani, who was elected president last month. He’s part of the clerical establishment that has run Iran for the past three decades. So it’s premature to assume that Rouhani’s election signals any breakthrough in stalled negotiations over Iran’s nuclear program.

But Rouhani’s victory does tell us something about the Iranian public mood: Among the six candidates who ran in the June 14 election, Rouhani was the most critical of the status quo; he called for reforms and new ties with the West. The fact that he won 51 percent of the vote (with a 73 percent turnout) marked a break from the tutelage of Supreme Leader Ali Khamenei, who appeared to favor national security adviser Saeed Jalili.

“We have no other option than moderation,” Rouhani said during the campaign. What this will mean in practice isn’t clear, but Rouhani has urged in his writings that Iran engage with the West, rather than depend on Russia and China.

Protesters have also shaken the Islamic populism of Turkish Prime Minister Recep Tayyip Erdogan. He has been an “authoritarian rock star,” in the words William Dobson, the author of “The Dictator’s Learning Curve.” But even Erdogan triggered a backlash after years of squeezing the Turkish media, courts and military. “The shared experience of repression, combined with collective frustration at mounting top-down efforts to regulate public life … brought citizens from different walks of life together” in Turkey, wrote Emiliano Alessandri, Nora Fisher Onar and Ozgur Unluhisarcikli on the Foreign Affairs website.

This new wave of activism in the Middle East isn’t pro- or anti-American. It’s something else — a movement of empowered citizens who don’t want the old secular dictatorships of Hosni Mubarak’s era, and don’t want a new Islamic authoritarianism, either. This core of “people power” surfaced in the initial “Arab Spring” of 2011, but a chill developed as the Muslim Brotherhood gained control in Egypt, and chaos prevailed in Libya and Syria. Despite these setbacks, this week showed there is still a popular movement for democratic change that resists dictation from anyone.

“I have never seen anything like this, not even during February of 2011. This is a genuine popular movement, no organisation whatsoever,” tweeted Egyptian writer Bassem Sabry late Tuesday.

For U.S. officials, recent events are a reminder that the Middle East is still in the early stages of a long-running process of transformation. Morsi’s election in 2012 offered the Muslim Brotherhood a chance to show that it could govern Egypt effectively. It has flunked the test — and the Egyptian military has lost patience with the failed experiment.

On America’s Independence Day, we celebrate the triumph of our democracy. But David McCullough reminds us in his book “1776” that in January of that revolutionary year, George Washington despaired that “few people know the predicament we are in.” It took America another 12 years to write and ratify a workable Constitution. In the Middle East, the convulsive democratic transition is just beginning.