These are a few (essentially worthless) coins I picked up.
The first three are from the French Mandate of Syria. Lebanon had just been split from the territory and the two countries under French control became l'Etat de Syrie and l'Etat du Grand Liban. (The latter is "grand" because today's Lebanon includes some regions around the original Lebanon as well.)
And these are coins from the British Mandate of Israel/Palestine. (I don't know how they dealt with Iraq currency-wise.)
The currency was the Palestine Pound which was equal to the British Pound but was decimalised. Instead of 12 pence to the shilling and 20 shillings to the pound, the currency was subdivided into 1000 "mils" ("milim" in Hebrew). Note that 1 pound in 1942 was approximately the equivalent of 40-50 pounds today and hence 2 mils were a usable 10 New Pence.
Bank notes existed as well (printed by a private bank in London). I wrote about those here.