Zhong Zhong and Hua Hua were the result of 79 nuclear transfer attempts. Two other monkeys were initially cloned from a different type of adult cell, but failed to survive.
Dr Sun said: "We tried several different methods, but only one worked. There was much failure before we found a way to successfully clone a monkey."
The research is reported in the latest edition of the journal Cell.
Cloned monkeys would allow scientists to study "a lot of questions" about primate biology, Dr Sun stressed.
Zhong Zhong all wrapped up at the laboratory in China
PA
He added: "You can produce cloned monkeys with the same genetic background except the gene you manipulated. This will generate real models not just for genetically based brain diseases, but also cancer, immune or metabolic disorders and allow us to test the efficacy of the drugs for these conditions before clinical use."
The scientists insisted they followed strict international guidelines for animal research, set by the US National Institutes of Health.
Co-author Dr Muming Poo, another member of the Chinese Academy of Sciences team, said: "We are very aware that future research using non-human primates anywhere in the world depends on scientists following very strict ethical standards."
British cloning expert Professor Robin Lovell-Badge, from The Francis Crick Institute, London, said he did not believe the research increased the chances of humans being cloned.
He said: "The work in this paper is not a stepping-stone to establishing methods for obtaining live-born human clones.
"This clearly remains a very foolish thing to attempt. It would be far too inefficient, far too unsafe, and it is also pointless. Clones may be genetically identical, but we are far from only being a product of our genes."
Technically Zhong Zhong and Hua Hua are not the first primate clones. That title goes to Tetra, a rhesus monkey born in 1999 through the much simpler method of embryo splitting that does not employ DNA transfer.
It is the same process that leads to the birth of natural twins, but can only generate up to four offspring at a time.
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