We report on the results of a spectroscopic survey of the environments of the gravitational lens systems CLASS B1600+434 ( z _ { l } = 0.41 ,z _ { s } = 1.59 ) and CLASS B2319+051 ( z _ { l } = 0.62 ) . The B1600+434 system has a time delay measured for it , and we find the system to lie in a group with a velocity dispersion of 100 ~ { } { km } { s } ^ { -1 } and at least six members . B2319+051 has a large group in its immediate foreground with at least 10 members and a velocity dispersion of 460 ~ { } { km } { s } ^ { -1 } and another in the background of the lens with a velocity dispersion of 190 ~ { } { km } { s } ^ { -1 } . There are several other small groups in the fields of these lens systems , and we describe the properties of these moderate redshift groups . Furthermore , we quantify the effects of these group structures on the gravitational lenses and find a \sim 5 \% correction to the derived value of H _ { 0 } for B1600+434 .