  In this paper, we consider periodic predator-prey systems of Leslie-Gower or
Holling-Tanner type, assuming that the coefficients are continuous positive
$\omega$-periodic functions. We prove an existence of positive
$\omega$-periodic solutions by means of operator method in Banach spaces with
cones. No constructive conditions are required for the coefficients, besides
the positivity and periodicity. At the end we point out that the used approach
can be applied with minor changes for proving the existence of positive
$\omega$-periodic solutions even in the case of certain delays.
