The electron-electron distribution function P(r(ij)) has been evaluated in closed form for the S-2 states of three-electron systems that are described by Hylleraas-type wave functions. The function P(r(ij)) can be reduced to the form P(r(ij)) = Sigma(I=1)(3) Sigma(k=1)(gI) A(IK)r(ij)(K)e(-alpha Irij). Numerical values of the expansion coefficients A(IK), Summation limits g(I), and exponents alpha(I) are determined for the ground states of selected members of the lithium isoelectronic series. A discussion is given on the necessary conditions that must be imposed on the basis set in order that P(r(ij)) be given by the analytical formula presented above. Expectation values for several moments (r(ij)(n)) and (delta(r(ij))) are evaluated.