[R] Overlapping axis numbering and labels when using par(new=TRUE)?

[mviljamaa]

I'm trying to plot two data sets on the same plot by using 
par(new=TRUE).

However this results in the axis numbering and labels being plotted 
twice as seen in the following picture:

http://i.imgur.com/4b1sNIc.png

How can I get the axis numbering and labels to not overlap? I could also 
manage with plotting only the axis numbering and labels of the other 
plot, but not of the other.