By Jon Leyne BBC News, Cairo

Doubts have been raised about Egypt's 82-year-old president's health and whether he will be fit enough to stand for re-election in 2011. Various factions might hope to step into any political vacuum and it is possible power could shift to his son.

Cairo at night is full of activity

It has not taken me long to learn that Cairo is not an early-morning city.

Even at the laundry I use - usually a paragon of hard work - there is no sign of anyone even at the respectable hour of 1030.

It is not until late in the evening that the city really wakes up. Then it will continue throbbing with life well into the early hours.

The cafe tables out on the street are full of men smoking the shisha (or hubbly-bubbly as it is known in English), drinking tea and playing backgammon.

Garishly lit shops continue selling toys or shoes, sweet pastries or plumbing supplies until well after midnight.

Outside the riverboat restaurant night clubs, I regularly see the queue of taxis collecting revellers, when business finally ends as the sun rises.

Gamal Mubarak is known as a child of privilege who has grown up in the presidential palace

So it was that I found myself driving through the narrow and crowded streets of one of Cairo's poorest neighbourhoods, to a political rally that did not begin until after the final evening prayers had finished echoing around from the surrounding mosques.

Local politicians had spent money on posters, a video, a sound system and refreshments, as they amassed signatures for a "popular" campaign to persuade Gamal Mubarak (son of the president) to stand for the presidency himself.

If that sounds a contradiction, well, it is.

Gamal Mubarak is known as a child of privilege who has grown up in the presidential palace.

He took his wife to Britain recently so they could have their child born there, rather than risk an Egyptian hospital.

Yet the organisers of this "popular upsurge" told me they wanted him because Egypt needed "change" or, better still, to break out of control by the "elite".

Gamal Mubarak is a senior officer of the ruling National Democratic Party

No wonder there is a high degree of scepticism about exactly how spontaneous this campaign really is, or how much it has official backing.

Hosni Mubarak has been in power now for 29 years. He says he has brought stability - others say, stagnation.

Take the example of the lifts in my office building. Since I arrived, two out of three of them have almost always been out-of-order.

When I suggested taking a tougher approach with the landlord, I was told it was not quite that simple.

The building itself was nationalised in the dramatic decade that followed the revolution of 1952.

Decay

Then the government imposed rent controls. The only people who benefit from that now are the (mostly wealthy) sitting tenants who pay just a few dollars a month for their tenancies, making a handsome profit subletting their apartments to people like us.

So nobody has any incentive to spend money on maintenance and the city centre is scarred by a series of beautiful old buildings, rotting into decay.

Similarly, the political system - born of a revolution 50 years ago - is now characterised by the inability to change.

That plays out in widespread poverty and illiteracy, as well as a shocking suicide rate. Around 5,000 people take their lives every year, as they give up on the battle to make ends meet.

President Hosni Mubarak has been re-elected five times since 1981

At another late-night political meeting, I met the former UN nuclear chief and Nobel Peace Prize winner, Mohamed ElBaradei.

He has returned to Egypt to lead a campaign to open up and democratise the political system.

By contrast with the bemused crowd watching the pro-Gamal rally, Mr ElBaradei's appearance attracts a throng of eager young people.

One of them is using a tiny camera to send out a live webcast of the earnest question-and-answer session.

Another dynasty

Mr ElBaradei insists that he is not a candidate for president.

Even under a fair and free election, there would be doubts about how much popular support he could muster. In any case, under the present arcane rules, he is not eligible to stand.

In fact about the only remotely credible candidate who does fit the rubric is - surprise, surprise - Gamal Mubarak.

It all appears to point in one direction - yet another dynastic succession in the Arab world.

Mohamed ElBaradei says he has nearly a million signatures of support

But if we are now seeing a testing of the waters, there seems to be an enormous lack of self-confidence about Gamal's possible candidacy.

Are there splits in the ruling party? Is the military opposed? Is his father sceptical that his smart-suited son has inherited his political nous and street savvy? What do the Americans think?

Everyone knows that the banned opposition Muslim Brotherhood is waiting in the wings, ready to test the young man, perhaps to destruction.

In sum - for whatever reason, for the first time in decades - no-one in Egypt has any idea what is going to happen next.

But I can report that, for a couple of brief days recently, all three lifts in my building mysteriously became operational.

Though one of them does occasionally require a sharp kick to make it work.

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