  We study a two-dimensional effective orbital superexchange model derived for
strongly correlated e_g electrons coupled to t_{2g} core spins in layered
manganites. One finds that the ferromagnetic and antiferromagnetic correlations
closely compete, and small changes of parameters can switch the type of
magnetic order. For the same reason, spin order is easily destroyed with rising
temperature, while alternating orbital correlations can persist to temperatures
where FM order has already melted. A scenario for the AF phase observed in
LaSrMnO_4 is presented.
