They are supposed to function as Hamas's military: an enigmatic commando force carrying out attacks against Israel and protecting the Islamist group's political leadership.
But Palestinian leaders, political analysts and human rights groups in Gaza say the powerful Qassam Brigades have grown unwieldy, increasingly defiant of Hamas political leaders and brutally repressive towards public dissent. Instead of focusing on Israel, they say, the Brigades have been trying to consolidate their power in Gaza.
Their role could complicate the reconciliation accord struck between Hamas and its former foe, Fatah.
"It's clear now that they control the political system, 100 per cent," a former intelligence leader who used to work for the Palestinian Authority said in an interview with The National.
"They control the policy-making. They have their own hierarchy and budget, and they aren't integrated into the government."
He and other analysts say the group increasingly resembles Iran's Revolutionary Guards. Created to protect the Islamic Republic's theocratic leadership, the Guards turned into a political and economic force.
While much of the Brigades' money is believed to come from Iran and Syria, they also earn significant revenue from their control over many of Gaza's bustling smuggling tunnels, which bring in from Egypt goods and weapons to circumvent Israel's blockade.
"The Brigades have become like warlords," said Mohammed Hejazi, an expert on political Islam in Gaza. "They have the money and the weapons, so they have the ultimate power."
In March, Brigade commandos surrounded the home of Ismail Haniyeh, Hamas' prime minister, after he invited the Palestinian Authority president Mahmoud Abbas to visit Gaza.
The move was interpreted as a warning to Mr Haniyeh and those in the Hamas leadership who expressed interest in reconciling with Fatah.
Hamas routed Fatah from Gaza in 2007. Since then, Hamas has ruled Gaza and Fatah has governed the West Bank.
Reconciliation threatens not only Hamas' monopoly on power, but also the Brigades' businesses, Mr Hejazi said.
"I wouldn't be surprised if the Brigades eventually foment their own coup in Gaza, because for them, Gaza is the golden egg," he said.
Israel's military has taken note of the discord between Hamas politicians and the Brigade. The group fired rockets into Israel shortly after Mr Haniyeh's invitation to Mr Abbas. The attack was widely thought to be a deliberate attempt to scuttle the Palestinian president's visit by provoking an Israeli counter-attack.
Speaking to the media last month about the increase in rocket fire from Gaza, an Israeli commander suggested that the Brigades were defying Hamas' political leaders.
Hamas political leaders, as well as Brigades members, insist that Brigades commanders take orders only from the political bureau. But Brigades leaders acknowledge that they are given significant leeway in how they carry them out. "It is a like a father-son relationship, and we are the son," said one Brigades commander, calling himself Abu Mohammed, during an interview at his home in the Gaza city of Rafah.
Even so, the Brigades operate in secrecy, ostensibly to protect them from Israeli attack. While Ahmed Jabari is considered the group's most powerful figure, its leadership structure is kept opaque. Nor do their members admit to being involved in the Brigades, which has an estimated 20,000 members who conceal their identities while operating in the field in their trademark black masks and green headbands.
Opposition politicians and human rights workers in Gaza accuse them of torture and other abuses, committed with virtual impunity and say they consist of members who adhere to particularly hardline interpretations of Islam.
At the same time, they point out, the frequency of Brigades' attacks against Israel are at their lowest in years despite recent rocket and mortar exchanges with the Israeli military.
"It's clear that Qassam is no longer in the business of resisting Israel, and so, it seems, their energies have turned to controlling the people of Gaza," said one rights researcher,.
He listed a number of incidents involving Brigades members where his organisation has asked Hamas, to no avail, for an investigation. This included the violent suppression of demonstrations in Gaza in March that called for reconciliation between Hamas and Fatah.
He also recounted another incident several months ago where a Brigades force stormed Shijayeh prison, engaging in a firefight with police, to free the family member of a Hamas leader.
Last year, he said, a woman filed a complaint against a Brigades leader whom she accused of torturing her. The official targeted the woman because he accused her of being a witch who had cast a spell that complicated his sex life. He eventually killed a relative of the woman after he discovered she had complained, the human rights worker said.
"We're in a situation now where the Brigades are only doing things that serve themselves," said Nasser Ahmed, a member of The Popular Front for the Liberation of Palestine faction in Gaza. "And all of Hamas is under the hand of the Brigades."
Khader Mihjez, a founding member of Hamas who eventually left the group, believes the group's political leadership has begun to compete for the loyalty of the Brigades. The problem, he said, is that the "loyalty of the Brigades to the politicians is not quite clear".
On the one hand, he said, its leadership seemed aligned with Hamas's Damascus-based leader, Khaled Meshaal, who is believed to control the Brigades' financing. But the group's younger recruits appear closer to Mr Haniyeh and the Gaza-based leadership.
The result, he concluded, has been a breakdown in Hamas' decision-making structure.
"So the important question to ask is not whether the Brigades are in control," Mr Mihjez said, "but whether they are out of control."
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