For strong electrolytes, according to Kohlrausch, molar conductivity decreases as the concentration increases.
( i don't know why I'm not allowed to attach a photo here in order to show you the diagram ), but however I'm trying to explain how the diagram looks.
In the diagram we have strong electrolytes like $\ce{HCl,\, H2SO4,\, KCl,\, LaCl3,\, Na2SO4}$ whose molar conductivity decreases as the concentration increases. But, what I don't understand is that in the diagram we have also $\ce{CH3COOH}$ which is a weak electrolyte, and his molar conductivity also is decreasing and even far more rapidly, as the concentration increases.
Can somebody explain this ?