Full details of the discoveries will be reported in the July bulletin of the Meteoritical Society, an international organisation devoted to the study of extraterrestrial material.
The two rocks are believed to be the 15th and 17th meteorites to be found from the Moon and Mars, respectively.
The lump of Moon rock, weighing in at about one kilogram (2.2 pounds), is thought to be the second largest Moon meteorite ever found.
The Mars rock is much smaller, weighing just 28 grams (one ounce).
The meteorite from Mars, dubbed Northwest Africa 480, was found in November in Morocco.
Famous rock
The Moon rock was bought in January in Morocco but is thought to have been found last year in neighbouring Algeria.
Full details of the discoveries will be reported in the July bulletin of the Meteoritical Society, an international organisation devoted to the study of extraterrestrial material.
If the Martian and lunar origins are verified, the rocks will be of considerable interest to scientists.
About 20,000 space rocks are estimated to land on this planet every year but very few hail from the Moon or Mars.
The most famous is the potato-shaped rock, known as ALH84001, which is at the centre of a debate over whether Mars once harboured life.