This paper deals with generalized Lotka-Volterra equations of the form \[ dx_ i(t)/dt=x_ i(t)\{b_ i(t)-a_{ii}(t)x_ i(t)- \sum^{n}_{j=1,j\neq i}a_{ij}(t)\int^{t}_{-\infty}K_{ij}(t- u)x_ j(u)du\}, \] i\(=1,2,...,n\); \(t>t_ 0\); \(t_ 0\in (- \infty,\infty)\) in which \(b_ i\), \(a_{ij}\) \((i,j=1,2,...,n)\) are continuous, periodic, and positive. The matrix kernel \(\{K_{ij}\}\) is integrable on [0,\(\infty)\), and verifies further technical assumptions. It is shown that periodic solutions do exist and estimates are found. Global asymptotic stability is also established for the periodic solutions with strictly positive components.