  A strong edge-colouring of a graph is a proper edge-colouring where each
colour class induces a matching. It is known that every planar graph with
maximum degree $\Delta$ has a strong edge-colouring with at most $4\Delta+4$
colours. We show that $3\Delta+1$ colours suffice if the graph has girth 6, and
$4\Delta$ colours suffice if $\Delta\geq 7$ or the girth is at least 5. In the
last part of the paper, we raise some questions related to a long-standing
conjecture of Vizing on proper edge-colouring of planar graphs.
