Next UN chief - the third world's Waldheim

Cautious. Thoughtful. Skillful. Unobtrusive. Basically decent. This is how many senior diplomats describe Javier Perez de Cuellar whom the Security Council has chosen to succeed Kurt Waldheim as United Nations secretary-general.

The softspoken Peruvian diplomat served as undersecretary-general of the UN for special political affairs and is intimately familiar with UN politics and mechanics.

His selection, which broke a six-week deadlock at the Council, is considered by most observers here as a victory in substance for the United States and for the Soviet Union against the small group of African radicals who, with China's support, wanted the post of secretary-general to go to a third-world activist like Tanzania's Salim Salim.

Only in the narrowest sense can it be argued that China had its way in as much as it managed to unseat Waldheim, who was favored by both superpowers, and replacehim with Perez de Cuellar.

Although the Peruvian diplomat, of noble Spanish ancestry, can be considered to be a representative from the third world in the narrow geographical sense, he is basically a product of Western culture and diplomatic tradition, and one of Waldheim's closest and most trusted aides.

The outcome of this protracted debate proved that at the UN as well as outside of it, the balance-of-power axis still runs East-West rather than North-South, in the opinion of veteran observers here. ''China was allowed to save face but it was not in a position, in the end, to modify the prevailing order,'' says a third-world diplomat.

Perez de Cuellar's prudent handling of such explosive issues as Cambodia, Afghanistan, and Cyprus, has gained him the respect and trust of the United States, Soviet Union, China, Pakistan, and the ASEAN countries. Great Britain and African countries were impressed by his fairness in supervising the elections in Zimbabwe.

Like Waldheim, Perez de Cuellar has demonstrated his diplomatic skills repeatedly and proven to the two superpowers that he knows how to avoid overstepping the bounds of his prerogatives. A Roman Catholic, a lawyer, a cultivated man, a good listener, a pragmatist, politically a liberal, he is in the words of one analyst, ''a man the West, the East, the South can live with.''

Perez de Cuellar served as Peru's ambassador to Moscow from 1969 to 1971. He traveled extensively with Waldheim to trouble spots the world over. His patience and subtlety are given credit, by high-ranking sources familiar with these problems, in bringing about some movement regarding Cyprus and Afghanistan.

Perez de Cuellar, who takes office Jan. 1, 1982, is expected by officials close to him to try to streamline the UN administration.

''Latin American problems will perhaps get greater emphasis, there will be more Spanish-speaking people in the upper UN strata, but otherwise the transition from Waldheim to Perez de Cuellar will be a smooth one,'' says a diplomat who is a friend of both. ''There will be no massive personnel replacements, no purges, no dramatic innovations,'' he says.

For Waldheim, who served the international community for 10 years with dedication and almost incredible energy, the failure to be reappointed to an unprecedented third term is sweetened by the fact that, with all their differences in temperament and style, his successor, whom he himself reared in UN affairs, is very much like himself - a believer in quiet but persistent diplomacy.