The head of the Jesuits, Father Peter-Hans Kolvenbach, was strolling in the Vatican Gardens when he spotted Cardinal Joseph Ratzinger beckoning to him. He hurried over only to be introduced to a clutter of feral cats fussing around the feet of the then Prefect of the Congregation for the Doctrine of the Faith. “You see, Father-General, this is the audience that listens to me,” joked Cardinal Ratzinger, the future Pope Benedict XVI.

This anecdote, which has been circulating among Jesuits in Rome for years, shows a good-humoured relationship between the “white pope”, who leads a billion Roman Catholics, and the so-called “black pope”, the name informally given to the leader of the Society of Jesus - not only on account of the colour of his attire but also because the Jesuits, with 19,200 members, are the largest and most influential order of the Church.

Earlier this month, a “black conclave” - the 35th General Congregation - opened in Rome to elect a successor to Father Kolvenbach, who, at 79, was allowed by the Pope to resign on grounds of age.

Such a retirement is unprecedented in the 473-year history of the order because black popes, like white popes, are expected to serve until they die. Pope John Paul II refused a similar request made in 1980 by Father Pedro Arrupe “for the good of the order and the good of the Church”. Arrupe did step down a year later, but only after a serious stroke.

Kolvenbach succeeded him in 1983, taking charge of an order troubled by a substantial number of individuals notorious for their disobedience to the teachings of the Church and to the Society of Jesus. A primary source of such discord was confusion over what was understood by the unique Jesuit fourth vow of loyalty in which members promise “special obedience” to the Pope “in regard to the missions”. This dates from the foundation of the Jesuits in the 16th century and it has allowed the pontiffs to ensure that what was effectively an elite force of intellectual missionary priests was always at the service of the universal Church.

But in the 1960s disputes arose over whether the vow referred to the Jesuits agreeing to go on missions wherever the Pope sent them, however dangerous, or if, as it had been understood for generations, the vow meant they had to embody and preach all that the popes taught. The ensuing chaos and distrust resulted in Pope John Paul II in 1981 suspending the governance of the Jesuits and temporarily appointing two of his own men to run the Society.

The Dutch-born Father Kolvenbach, a former Jesuit Provincial of the Middle East, was thought not to be John Paul's choice of leader, but he has proved to be extremely effective. Crucially, he has established dialogue between the Vatican and Jesuits in the field, and at the end of his 24 years of office relations between Rome and the Society are said, by Jesuit sources, to be the best they have been for years.

In particular, Benedict XVI is said to hold in “very high regard” the Society's educational institutions in Rome - the Pontifical Gregorian University and the Biblical Institute. His confidence in the Society has been reflected in Jesuit appointments such as his spokesman, Father Federico Lombardi, who in 2006 replaced Dr Joaquín Navarro-Valls, a member of Opus Dei.

If Arrupe gave the Jesuits new purpose with his focus on social justice, Kolvenbach has restored stability to the Society. The task of the new leader is to make the order missionary once again. Whoever is elected will have to confront a decrease in vocations in the West, which has seen Jesuit numbers decline by 3,000 in the past decade. Militant Islam, globalisation and aggressive secularism means he would be expected to spearhead the Church's efforts in the field of inter-religious dialogue, to continue to fight for justice for the world's poor and to take Christianity to new frontiers of faith and science and faith and culture.

There is no obvious crown prince waiting in the wings but there are strong candidates from every corner of the globe. European candidates can claim experience of Islam and secularism. Jesuits in Latin America are still at the forefront of fighting for social justice. The ten provinces of the US have provided the Vatican with a list of 42 potential candidates. For the first time, however, there is a possibility of a Jesuit leader emerging from South Asia, the region that now produces more Jesuit priests than any other part of the world (20 per cent of the total compared with 15 per cent in North America, formerly the largest sector).

Names in circulation include Father José Morales Orozco, rector of the Iberoamericana University in Mexico City; Father Mark Raper, head of the Jesuits in Australia; Father Orlando Torres, a former Puerto Rican Jesuit leader now based in Rome, and Italian Father Franco Imoda, a former rector of the Gregorian University and a psychologist believed to be highly regarded at the Vatican.

Father Kolvenbach's resignation was formally accepted by his fellow Jesuits on Monday (Jan 14). The new leader may be elected as early as today by the votes of the 217 delegates from around the world at the end of four days of prayer. Unlike the white pope he will have no right to turn down his new office.

The General Congregation itself is expected to run until the end of March as the Jesuits attempt to set out the objectives of the order in the years ahead.

Pope Benedict will address the Jesuits at the end of their deliberations. He has limited his intervention primarily to asking them to arrive at a definitive clarification of what is meant by the fourth vow, which has been listed by the Jesuits for discussion under the theme “apostolic obedience”.

It is likely that this Pope wants to bury the controversies of the past for good, and that he wants the Jesuits to seize the opportunity to return fully to their charism of “thinking with the mind of the Church”, so that once again they may unleash their missionary potential “Ad majorem Dei gloriam” - to the greater glory of God.