Argon-isotopic abundances were measured in neutron-irradiated samples of Martian meteorites Chassigny, Allan Hills (ALH) 84001, ALH 77005, Elephant Moraine (EET) 79001, Yamato (Y) 793605, Shergotty, Zagami, and Queen Alexandra Range (QUE) 94201, and in unirradiated samples of ALH 77005. Chassigny gives a Ar-39-Ar-40 age of 1.32 +/- 0.07 Ga, which is similar to radiometric ages of the nakhlites. Argon-39-Argon-40 data for ALH 84001 indicate ages between 3.9 and 4.3 Ga. A more precise definition of this age requires detailed characterization of the multiple trapped Ar components in ALH 84001 and of Ar-39 recoil distribution. All six shergottite samples show apparent Ar-39-Ar-40 ages substantially older than the similar to 165-200 Ma range in ages given by other isotope dating techniques. Shergottites appear to contain ubiquitous Ar components acquired from the Martian atmosphere, the Martian mantle, and commonly terrestrial atmospheric contamination. Zagami feldspar also suggests inherited radiogenic Ar-40. These data analyses indicate that the recent Martian atmospheric component trapped in shergottites has a Ar-40/Ar-36 ratio, possibly as low as similar to 1750 and no greater than similar to 1900. These ratios are less than the value of 3000 +/- 500 reported by Viking. The Ar-40/Ar-36 ratio for the Martian mantle component is probably <500 but is poorly constrained. The correlation between trapped Ar-40/Ar-36 and Xe-129/Xe-132 in shergottite impact glasses and unirradiated samples of ALH 77005 shows considerable scatter and suggests that the Ar-36/Xe-132 ratio in the Martian components may vary. Resolution of Martian atmospheric 40Ar/36Ar ratio at different time periods (i.e., at similar to 4.0 and 0.2 Ga) is also difficult without an understanding of the composition of various trapped components.