Can i run norton 360 and avg pc tuneup concurrently

I have been running norton 360 for a number of years now, currently version  and now i am running the norton 360.  Would there be any problems with me installing AVG PC Tuneup in order to speed up my computer which seems to be running really slow?  i only ask this as after installation of both my computer is taking about 5 mins to start.  All advise appreciated.