1) "Leviathan. — The word Leviathan (Hebrew, líweyãthãn), which occurs six times in the Hebrew Bible, seems to have puzzled not a little all ancient translators. The D.V. has kept this name, Job, iii, 8; xl, 20; Is., xxvii, 1; it is rendered by dragon Ps. lxxiii (Hebr., lxxiv), 14, and ciii (Hebr., civ), 26; The word leviathan means: (1) crocodile (Job 40:20 and Psalm 73:14); (2) a sea-monster (Psalm 103:26, Isaiah 27:1); (3) possibly the Draco constellation (Job 3:8). (4) a Dinosaur, possibly the Kronosaurus." 2) "Behemoth, is generally translated by "great beasts"; in its wider signification it includes all mammals living on earth, but in the stricter sense is applied to domesticated quadrupeds at large. However in Job, xl, 10, where it is left untranslated and considered as a proper name, it indicates a particular animal. The description of this animal has long puzzled the commentators. Many of them now admit that it represents the hippopotamus, some Young Earth Creationists think it's a dinosaur like the Apatosaurus or the Brachiosaurus, so well known to the ancient Egyptians; it might possibly correspond as well to the rhinoceros." Source and further information: http://en.wikipedia.org/wiki/List_of_the_animals_in_the_Bible

No one knows. The terms, if they do indeed refer to dinosaurs, as many hold, are not indicative of any particular species. Remember that dinosaur species have only been identified in the last few centuries. The Leviathan was some sort of sea monster. If it was a dinosaur, and not a whale, then it would be something like a plesiosaur, I suppose. The Behemoth, if it is a dinosaur and not a hippo, could be something like a brachiosaurus, as it would appear that the behemoth was a herbivore.

LEVIATHAN [Heb., liw·ya·than´]. This Hebrew word occurs six times in the Bible. It is believed to come from a root word meaning “wreath”; hence the name indicates something that is “wreathed,” or “gathered into folds.” The word is transliterated in most Bible translations. Since, with the exception of Job 3:8, the references mention water in connection with it, Leviathan appears to signify some form of aquatic creature of great proportions and strength, although not necessarily of one specific kind. Psalm 104:25, 26 describes it as cavorting in the sea where ships travel, and for this reason many suggest that the term here applies to some type of whale. Though whales are rare in the Mediterranean, they are not unknown there, and parts of two whale skeletons can be found in a museum at Beirut in Lebanon. An American Translation here says “crocodile” instead of Leviathan. Additionally, the word “sea” (yam) by itself is not determinative inasmuch as in Hebrew it can refer to a large inland body of water such as the Sea of Galilee (Sea of Chinnereth) (Nu 34:11; Jos 12:3), or even to the river Nile (Isa 19:5) or the Euphrates.—Jer 51:36. The description of “Leviathan” at Job 41:1-34 aptly fits the crocodile, and the “sea” of verse 31 may refer to a river such as the Nile or another body of fresh water. It should be noted, however, that some crocodiles, as the Nile crocodiles (Crocodylus niloticus), are found along the seacoast and at times go out into the sea some distance from land. _______________________________________________ BEHEMOTH (Be·he´moth). The designation “Behemoth,” appearing at Job 40:15, has been variously viewed as (1) a derivative of an Egyptian word for “water ox,” (2) a word possibly of Assyrian origin meaning “monster,” and (3) an intensified plural of the Hebrew word behe·mah´ (beast; domestic animal) that is understood to denote “great beast” or “huge beast.” In the Greek Septuagint the word the·ri´a (wild beasts) translates the Hebrew behe·mohth´. Evidently, though, a single animal is meant, as is indicated by the fact that the description given of Behemoth is not that of several creatures but of only one, generally considered to be the hippopotamus (Hippopotamus amphibius). In fact, a number of Bible translations (AT, La, Ro, NW, JB, RS) use the word “hippopotamus” in the main text or in footnotes to identify the creature referred to by God. The hippopotamus is a huge, thick-skinned, almost hairless mammal that frequents rivers, lakes, and swamps. It is noted for its short legs, huge jaws, and large head, which is said to weigh up to a ton. So great is the power in its jaw and teeth that one bite can pierce the armor of a crocodile. Full grown it may be 4 to 5 m (12 to 15 ft) long and may weigh up to 3,600 kg (8,000 lb). An amphibious creature, the hippopotamus, in spite of its prodigious size, can move relatively fast both in and out of water. It feeds on soft water plants, grass, reeds, and bushes, each day taking more than 90 kg (200 lb) of greenery into its 150- to 190-L (40 to 50 gal) stomach. At one time the hippopotamus was found in most of the large lakes and rivers of Africa, but, as a result of man’s hunting, it has disappeared from many regions and is said to be unknown N of the cataract at Khartoum, Sudan. In ancient times the hippopotamus may even have frequented the Jordan. In fact, it is reported that tusks and bones of this creature have been found in various parts of Palestine. The description in the 40th chapter of the book of Job offers a vivid word picture of this huge mammal, Behemoth. It is described as being herbivorous. (Vs 15) The sources of its tremendous power and energy are noted to be in the hips and in the tendons of its belly, that is, the muscles of its back and those of its belly. (Vs 16) The tail of Behemoth is like a cedar. Since the tail of a hippopotamus is fairly short, measuring about 46 to 51 cm (18 to 20 in.), this is likely to be understood as meaning that the animal can set its thick tail rigidly upright or swing it about like a tree. “The sinews of its thighs are interwoven,” so that the fiber and tendons of muscles of its thighs are twisted together and braided like powerful cables. (Vs 17) The bones of its legs are as strong as “tubes of copper,” thus being able to support the great weight of the body. The bones and ribs are like wrought-iron rods. (Vs 18) The Behemoth’s immense consumption of food is alluded to (vs 20), and mention is made of its relaxing under the thorny lotus trees or concealing itself in a swampy place, beneath the shade of the poplars. (Vss 21, 22) Even when a river overflows its banks, this creature does not panic, for it can still keep its head above the level of water and swim against the force of the deluge. (Vs 23)

The Hebrew word "tanniyn" pronounced ta-neen, means (dragon) and is first written is Scripture before 1400 BC. This would be the equivalent to the modern name dinosaur. The name Behemoth was first used before 1400 B.C. as well and the way it is described in the Book of Job 40:15-24, could very well be a Brachiosaurus. Leviathan was first used before 1400 B.C. and because of the description of it as given in Job chapter 41, it could very well be describing a Kronosaurus. Leviathan is also found in Psalm 104:25,26, and Isaiah 27:1.