The object of the present paper is first to point out a hitherto unnot
iced relationship between two seemingly different families of generali
zed elliptic-type integrals which were studied recently. This relation
ship and some other simple techniques are then employed in order to de
rive many properties (including, for example, analytic continuations a
nd asymptotic behaviors) of these families. Several interesting specia
l cases, involving simpler elliptic-type integrals, are also considere
d.