  SrEr$_2$O$_4$ has been characterised by low-temperature powder neutron
diffraction, as well as single crystal specific heat and magnetisation
measurements. Magnetisation measurements show that the magnetic system is
highly anisotropic at temperature above ordering. A magnetic field of 280 kOe
applied at $T=1.6$ K does not overcome the anisotropic magnetisation and fails
to fully saturate the system. Long range antiferromagnetic ordering develops
below $T_N=0.75$ K, identified by magnetic Bragg reflections with propagation
vector ${\bf k}=0$ and a lambda anomaly in the specific heat. The magnetic
structure consists of ferromagnetic chains running along the \textit{c} axis,
two adjacent chains being stacked antiferromagnetically. The moments point
along the \textit{c} direction, but only one of the two crystallographically
in-equivalent Er sites has a sizeable ordered magnetic moment, 4.5 $\rm \mu_B$
at 0.55 K. The magnetic properties of SrEr$_2$O$_4$ are discussed in terms of
the interplay between the low-dimensionality, competing exchange interactions,
dipolar interactions and low lying crystal field levels.
