GAZIANTEP, Turkey – The Islamic State’s vaunted exercise in state-building appears to be crumbling as living conditions deteriorate across the territories under its control, exposing the shortcomings of a group that devotes most of its energies to fighting battles and enforcing strict rules.

Services are collapsing, prices are soaring and medicines are scarce in towns and cities across the "caliphate" proclaimed in Iraq and Syria by the Islamic State, residents say, belying the group’s boasts that it is delivering a model form of governance for Muslims.

Slick Islamic State videos depicting functioning governing offices and the distribution of aid fail to match the reality of growing deprivation and disorganized, erratic leadership, the residents say. A trumpeted Islamic State currency has not materialized, nor have the passports the group promised. Schools barely function, doctors are few and disease is on the rise.

In the Iraqi city of Mosul, the water has become undrinkable because supplies of chlorine have dried up, said a journalist living there, who spoke on the condition of anonymity to protect his safety. Hepatitis is spreading and flour is becoming increasingly scarce, he said.

"Life in the city is nearly dead, and it is as though we are living in a giant prison," he said.

In the Syrian city of Raqqa, the group’s self-styled capital, water and electricity are available for no more than three or four hours a day, garbage piles up uncollected, and the city’s poor scavenge for scraps on streets crowded with sellers hawking anything they can find to sell, residents say.

Videos filmed in secret by an activist group show desperate women and children clamoring for handouts of food, while photographs posted on the Internet portray foreign jihadists eating lavish spreads, a disparity that is starting to stir resentment.

Much of the assistance that is being provided comes from Western aid agencies, who discreetly continue to help areas of Syria under Islamic State control. The United States funds health-care clinics and provides blankets, plastic sheeting and other items to enable the neediest citizens to weather the winter, a U.S. official said, speaking on the condition of anonymity because of the sensitivity of the subject.

The government workers who help sustain what is left of the crumbling infrastructure, in Syrian as well as Iraqi cities, continue to be paid by the Syrian government, traveling each month to collect their pay from offices in government-controlled areas.

"ISIS doesn’t know how to do this stuff," said the U.S. official, using an acronym for the group. "When stuff breaks down, they get desperate. It doesn’t have a whole lot of engineers and staff to run the cities, so things are breaking down."

There are also signs of falling morale among at least some of the fighters whose expectations of quick and easy victories have been squashed by U.S.-led airstrikes. A notice distributed in Raqqa this month called on fighters who were shirking their duties to report to the front lines, and a new police force was created to go house-to-house to root them out.

There is no indication that the hardships are likely to lead to rebellion, at least not soon. Fear of Draconian punishments and the absence of alternatives deter citizens from complaining too loudly, the residents said.

But the deterioration is undermining at least one important aspect of the Islamic State’s self-proclaimed identity – as a state, dedicated to reviving the seventh-century caliphate that once ruled the Muslim world.

Governing is as central to that goal as the military conquests that occurred as Islamic State fighters swept through much of Syria and Iraq over the past year.

The group’s momentum on the battlefield has been slowed by the U.S.-led air campaign, which has helped reverse or stall Islamic State offensives on numerous fronts.

That the group is also failing to deliver services in the areas it does control calls into question the sustainability of its larger ambition.

The Islamic State "is not this invincible monster that can control everything and defeat everyone," said an activist in the eastern Syrian city of Deir al-Zour, who also spoke on the condition of anonymity to describe the ineffectual delivery of services there.

"The whole idea that it is well organized and an administrative entity is wrong. It is just an image."