The Chrysler Corporation cabs were all Perkins 4.99 "Mirage" engined [many build or converted in Belgium]. The early 1950s ones were DeSotos. Then there were late 1950s long wheelbase cars ["stretched"] which were, if my memory does not deceive me, Plymouth Fury based. I don't know whether those were factory built stretch version or whether they were sub-contracted to one of the US stretch limo specialists. The last Furies of this configuration were sold in the late 60s early 70s. All the above were built to comply with (old) Israeli regulations allowing such vehicles to carry 7+1 passengers.
In the late 1960s, Chrysler lost interest as Checker gained this market (until ruined by the dreadful early GM diesel). The Checkers were slow, shaky and noisy. They used to operate them mainly between major towns in competition with buses and mini-buses!
The Dodge Dart / Plymouth Valiant twins were very popular in Israel at one stage and were thought of as an executive's car. 90% were slant sixes, but I distinctly remember a few Demons and Dusters with 273 and 318 family v-8 engines in them.
My father had a 1971 Dart. The car was tough as nails: It went with him to the 1973 war, came back and was not sold until 1976, at which time not much was wrong with it! Yes, they were also used by the government and the IDF. Some of the Valiants stayed with the navy until 1982: 22 years. I think all the IDF had was Valiants for some reason. Not surprising, as they all shared the slant six with the Israeli-produced version of the Weapons Carrier/Power Wagon and the larger D-series pickups and trucks, which, for anybody serving in the late 1970s and early 1980s were a familiar experience. Those were produced (and assembled) in Nazareth until the early 1980s. Some pictures of the military stuff on this site (Israeli produced Weapons Carrier the fabled "Nun-Nun"). The Nazareth factory is making those now (engine is the old AMC six).
The Weapon Carriers were ultimately developed into the Abir and eventually replaced by the Hummer. Oh, and they made a rear engined armoured car which, like the Swiss Mowag, was Power Wagon based.
Other than that, if you were really filthy rich, there was always the bigger Coronet, Fury and - real rarities those - some Barracudas with proper engines in them (383) as well as (very, very few) exotic things like Chargers. Those cars were always losing out to the Pontiac Trans Am however.
The Volare was also popular at one stage but the build quality wasn't there any more. As for the K-cars, [the Saratoga was sold in Israel among others.] Nowadays Chrysler has made a comeback with the Neon and the 4x4s, but the bigger cars are too expensive when compared with the GM (Chev & Buick) offerings.
[later] Frontal photo of the Abir (the final version of the Power Wagon) has now appeared on the IDF Modeling site (no shortage of opportunity now that things are the way they are). Looks like no Dodge you've ever seen, but the lineage is there. I think the bathtub shaped body is designed to minimize mine damage. 'Every trip an adventure'.
The Israeli electrical power supplier 'Hevrat Hahashmal' (try saying that and see what happens) used the big Dodge trucks, I'm not sure what series, but they were the heaviest model you could get (C cabbed), were painted the same color gray power poles were and, I think, in service until the late 70s. However, Dodge never found real acceptance on the heavy duty field, mostly it was in the up to 3T area.
Israeli generals used to have Valiants; the commander of the Israeli Defense Force had a Dart (we don't know if it was a Valiant-based Dart or a B-body, though).
The Valiant was a common getaway car for Israeli bank robbers. Ben-Gurion, the first Prime Minister, had a Polara, which is now in a museum.
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