The author studies the stability of the Ritz-Volterra projection and derives \(L^ \infty\) error estimates for finite element methods for Volterra integro-differential equations of the form \(u_ t+A(t)u+\int^ t_ 0 B(t,\tau)u(\tau)d\tau=f\), with given initial and (homogeneous) boundary conditions. Here, \(A(t)\) is a symmetric positive definite elliptic operator and \(B(t,\tau)\) is an arbitrary second-order linear partial differential operator with smooth coefficients. The results in this paper are closely related to those in Y. Lin, V. Thomée and L. B. Wahlbin [SIAM J. Numer. Anal. 28, No. 4, 1047-1070 (1991; Zbl 0728.65117)].