For the first time in many years, a few young women are appearing on the streets of central Cairo with their faces hidden behind the traditional veil. Many more have adopted somber long dresses that cover all parts of the body except the face.

At kiosks in many cities, tapes of sermons by Sheik Abdel Hamid Kishk, a popular blind preacher of Islamic puritanism, are quickly purchased by his devoted followers.

On Islamic holy days, thousands of worshipers turn out at prayer services organized by the once-out-lawed Moslem Brotherhood, now so visible and well-organized that its posters appear in the windows of Cairo buses and its thick glossy magazine is on every newsstand.

These are the visible signs of a resurgence of Islamic orthodoxy and puritanism that is one of the strongest trends in Egyptian society today. It has been under way for about three years, and appears to be gaining strength -- particularly in the universities.

Repelled by materialism and corruption, frustrated by the lack of political and economic opportunity, many of the 40 millior. Egyptians are seeking spiritual solace or an outlet for their energies in a campaign of Islamic fundamentalism. It goes beyond the deep and abiding piety of the average Egyptian farmer or workman into social and occasionally political activism.

Similar trends, in varying degrees, are sweeping across Moslem countries from Malaysia to North Africa.

In Iran, a rebellion spurred by the Moslem clergy has undermined the shah's power, but the Islamic revival here is different in cause and nature. Moslem intellectuals see it as the reappearance of a phenomenon that has occurred in periodic cycles throughout the Moslem world.

In universities throughout Egypt, fundamentalist Moslem students are demanding administrative changes that reflect their beliefs, such as separation of the sexes in the cafeterias. In the last round of student elections, orthodox Moslem candidates scored impressive victories.

The new speaker of the parliament, Sufi Abu Taleb, called in a representative of Al Azhar University, the seat of Islamic scholarship, to discuss bringing Egyptian public law into conformity with Sharia, or koranic -- a project for which there is growing sentiment in the parliament and in legal circles.

There is no Egyptian equivalent of the Iranian mullahs' implacable drive to bring down the shah. Here, the leading religious figures are appointed by and obligated to the government, and support it from the pulpit. They are themselves frequently the target of reformist criticism.

Government officials, intellectuals and journalists, while apprehensive about the appeal of the orthodox Moslem campaign, are frequently contemptuous of its adherents.

"Those people are having hallucinations," said a government official who was fuming over a story told by his wife, a doctor, about a female medical student who showed up for an oral examination with her face veiled.

"How can a doctor examine patients with her face veiled like that? She said it was her religious right. Well, the professor said it was his religious right not to give her the exam, and he won."

"Why do you want to know about Sheik Kishk?" A historian asked "He's just a fanatic. Nobody pays any attention to him."

That appears to be the prevalent attitude among urban, sophisticated Egyptians, even those who are themselves devout, who regard the fundamentalists as ludicrous or dangerous or both. Naturally it is not a view shared by participants in the movement.

"We are puritans, but we are not fanatics," said Omar Telmassani, editor of The Call, the monthly magazine of the Moslem Brotherhood. He spent 17 years in prison during the presidency of Gamal Abdel Nasser because of his membership in the Brotherhood, which had a reputation as an organization of terrorists who made two attempts on Nasser's life.

Islam, he said in an interview, "is a comprehensive system which regulates all aspects of human life. A Molslem can ind his political, social, economic and even family laws of conduct in our religion. Nobody can be a good Moslem who adopts some of the principles of Islam and not others."

Any scholar from Al Azhar or official of the Religious Affairs Ministry might say the same thing. The difference is that they are tolerant of, or complacent about, a political and social system in which those ideas are not put into practice, which the Brotherhood, similar organizations such as the Youth of Mohammed, and the student groups are not.

Recent issues of The Call have criticized the Camp David peace agreements, corruption in the government, the shah of Iran at a time when President Anwar Sadat was openly supporting him, and the failure of Egyptian judges to apply Islamic principles in their rulings. But Telmassani denied that the Brotherhood is opposed to Sadat's government.

Nasser, he said, "was a tyrant." But under Sadat, "we are only expressing our point of view. We are pledged and committed to the laws of the government, but the faith is something different."

That the government allows the Brotherhood and similar groups to operate is a measure of the delicate balance between public policy and popular religious sentiment that any Egyptian leader must find.

Islam is the state religion, but the individual Egyptian is generally free to be religious or not. Alcohol and pork are widely sold, men and women work side by side, shops and government offices keep running right through the call to prayer, and the legal code is substantially independent of Sharia.

No political party based on religious affiliation is permitted. Sadat has promised the Christian minority that they will never be subjected to Sharia, the harsh legal system prevalent in Saudi Arabia. Nasser broke much of the power of the traditional Islamic institutions, such as Al Azhar, by bringing them under government control.

Nevertheless, Islam remains a powerful force in Egypt that no government can ignore, and the pressure from the fundamentalists is being felt in such responses as the current anticorruption campaign.

Sadat often prays in public, demonstrating his piety, and he alludes to religious motivation in speeches on policy. He is reliably reportedly to have struck a bargain with the leaders of the Moslem establishment, such as the shieks of Al Azhar, by which he tolerates their criticism on issues such as family planning provided they refrain from undermining him politically as the Iranian mullahs have done to the shah.

It is always made clear when any religious group or individual is going too far.

Shiek Mohammed Sharawy, for example, had a religious television program that was so popular he began to acquire a personal following. Sadat's response was to make him the minister of religious affairs, tucking him safely out of the way and impairing credibility with the Moslem faithful who viewed the government as corrupt.

When a truly fanatical group known as the Migration and Atonement Society surfaced in 1977 by kidnaping and murdering a former minister of religious affairs, the government wasted no time examining the sincerity of the members' religious sentiments.

Ignoring the members' claims that Egyptian government and society were corrupt and heretical, Sadat ordered them tried by a military court, and the leaders were promptly executed.

By all accounts, the group's principles and its act of violence brought revulsion and abhorrence from the vast majority of Egyptians -- a fact often cited by those who believe that the current Islamic surge will have only limited impact on the way the country operates.