A more forceful, hard-working set of individuals would be difficult to find in Latin America - or indeed anywhere. The family has gone from the dust of a poor Syrian village, via one of the most unpromising pieces of semi-desert on the eastern flanks of the Andes, to some of the most powerful positions in the Western Hemisphere. All in two generations.
And on Tuesday the most prominent member of the clan, Carlos Saul, President of the Argentine Republic since 1989, sets foot for the first time on British soil as the guest of Her Majesty's Government, and will be breaking bread with Her Majesty herself later in the week. The Menems, as I observed when once making a film about them, are certainly industrious and determined.
The President's father, a devout Sunni Muslim, migrated from the village of Yabrut, not far from Damascus, to the New World, and made a precarious living in the dirt-poor province of La Rioja, buying everyday items in tiny towns, loading them on his donkey and selling them in tiny villages.
His sons were determined to climb up the greasy Argentine poll. At some time - the official biography does not record the exact date - Carlos was baptised as a Christian. Then he got close to General Juan Domingo Peron, the old tub-thumper who in his time as a president and as political exile had the same relationship to principled political beliefs that woodwork has to antique furniture.
He went back to Yabrut to meet nice Muslim girls - he is fond of girls - and came away with the fiery Zulema Yoma, who had in fact grown up not far from him in Argentina. They split up, but to this day she remains true to Islam.
The brave, aspiring Carlos was put in prison by a military government for his Peronist views but emerged triumphant to become governor of his province. In that job he spent provincial funds in creating jobs not just for the boys but for the girls and the babies, the mums and the dads, the old, the sick, the lame and the lazy, especially if they were members of his family.
When La Rioja's money was exhausted - a rapid process - he started printing his own. The La Rioja banknotes bore the head of a 19th-century hero but the image had an amazing similarity to that of Carlos Saul Menem, complete with extravagant sideburns. The Riojanos loved him.
He won the presidency in 1989. Overnight, the last of the big spenders became the driest monetarist. Overnight the former prisoner of the generals granted amnesty for those who had carried out the most Pinochetesque of atrocities on political prisoners in Argentina's dirty war in the Seventies. Overnight the presidential candidate who had sworn to retake the Falklands at whatever cost was cosying up to the British conquerors. With great cunning he changed the constitution to allow himself to stand for a second consecutive term, and won again handsomely in 1995. His brother Eduardo became a senator. This year he decided he would go for a third term - but with uncharacteristic modesty, and falling opinion polls, then dropped the idea.
This week he faces his greatest test. While in Britain he must do his best to mend relations with Britain after a war over the Falklands in 1982 that he did not start, but which he supported to the hilt at the time.
At the same time he must not be seen to be truckling to "Los Piratas" in London. No one in Argentina forgets that Britain mounted two bids to invade and seize Argentine at the beginning of the last century: though British officers had to haul down the Union Jack over Buenos Aires in 1805 and again in 1810, 19th-century Argentina was as much an economic colony of Britain as ever Canada and New Zealand were.
His task is immensely complicated by the arrest of the former Chilean dictator here. The relationship between giant Argentina, a country the size of Europe, and thin little Chile, its neighbour to the west, has been difficult and complicated. He cannot be seen to be gloating over Pinochet's fate - despite the fact that the Chilean general's help to the Royal Navy and the SAS virtually guaranteed Argentina's defeat in 1982. He must be secretly delighted that the former leader of his troublesome neighbour is - for the moment at least - in the care of our Metropolitan Police.
Menem comes to a country whose leaders have said that the question of sovereignty over the Falklands is not on the agenda. Yet he can't return home with absolutely no benefits for his side - whatever he may have said, with or without the assistance of Alastair Campbell, in Friday's Sun.
There will doubtless be a list of fairly meaningless tweakings of the regulations in force on both sides, on the question of the Falklands. These will be presented by diplomats as evidence of an amazing healing process .
But once the President has left Britain the Anglo-Argentine relations will doubtless sink back into the mire of grumbles and petty backbiting that has characterised them for years. We can only be thankful that the atmosphere is no worse than it is.Reuse content