Egypt's dynamic political situation has entered a new phase now that Hosni Mubarak has abandoned his 30-year-old presidency and handed the reins of power over to the military in the face of an 18-day wave of popular protests.

Whether the most populous Arab country will regain stability soon or remain mired in unrest remains to be seen. Pundits and observers in Egypt and beyond agree that what comes next depends on three critical variables.

WILL THE PARALYZING PROTESTS RECEDE SOON?

Weeks of nationwide protests have taken a heavy toll on the country's social stability and economic activity and people's everyday lives as well.

Now that Mubarak's resignation has met the key demand that protesters pressed, will the demonstrations end anytime soon? Under the current circumstances, the answer is probably No.

That's because following Mubarak's departure, protesters have raised new demands, demands that vary widely among the country's different factions.

For example, a group called "Jan. 25 Revolutionary Youth" has announced that it will continue "the revolution" until its demands are completely satisfied.

The conditions listed by the group, which has been demonstrating at Cairo's Tahrir Square, include the abolishment of the current constitution, the dissolution of parliament and the establishment of a transitional government.

Such a stance strikes a chord with many Egyptians long weary of government repression and corruption.

Ayman Nour, an opposition party leader, said he is looking forward to a transitional period "that will take us to a civilian state that will meet our legitimate demands of having a civilian, free country."

"I look forward to a transitional period of co-sharing of power between the army and the people," said Mohamed ElBaradei, a leading opposition figure and the former chief of the International Atomic Energy Agency.

WILL THE MILITARY BE ABLE TO CONTROL THE SITUATION?

The answer is yet to be found out. What's obvious is that a pile of daunting challenges now stand before the military, a powerful part of the state apparatus that includes around 500,000 active personnel.

An immediate priority for the military is to crack down on violent crime and terrorist plots, and rapidly restore social stability. Many runaway inmates are still at large, and extremists and terrorists will waste no time in exploiting Egypt's current upheaval to pursue their own agendas.

Meanwhile, the Egyptian army has never taken the helm of national politics before and thus, might lack adequate experience in running the country.

Therefore, the military must figure things out as soon as possible so as to keep Egypt's paralyzed political system and economy functioning while it overhauls the country for greater democracy.

Another challenge is that the military has to engage opposition parties in one way or another. With the opposition cranking out more demands, it remains to be seen whether the military will retain its stance of dialogue and cooperation. A standoff could occur should the two sides fail to accommodate their pursuits.

WILL THE PRESIDENTIAL ELECTION TAKE PLACE AS SCHEDULED?

The military's takeover of Egypt is an expedient measure. Facing huge domestic and foreign pressures, the ruling military has to quickly transfer power to a new president who, according to the Egyptian constitution, should be elected within 60 days of Mubarak's resignation.

Analysts say the military will face three serious challenges as it makes the necessary preparations for the election.

Firstly, the military has to prepare well the legal grounds that will pave the way for the presidential election.

During the massive protests that ousted Mubarak, amending the articles of Egypt's constitution related to the presidential election was one of the main changes protesters sought.

Before his resignation, Mubarak had agreed to amend the constitution to relax the qualification requirements for candidates and limit the tenure of the president.

However, now that Mubarak is gone, it is hard to say whether an amendment to the constitution can proceed smoothly.

Another challenge that the military has is to ensure a smooth presidential election.

The task will be a tough one. More parties than usual are expected to participate and that will make the balloting more complicated.

Differences also may appear on some issues, such as the formation of the election commission, the timetable, and procedures of the election as well as corresponding monitoring mechanisms.

The third challenge facing the military is ensuring that the outcome of the election will be accepted by everyone.

An acceptable outcome is a prerequisite for the peaceful transition of power, which the military wants. If any standoff develops after the election because of disputes over the results, it will be difficult for the military to hand over power as scheduled.