Asymptotics and Related Properties

Question

I have a rather general question: If there are two integer sequences such that $$\lim_{n\to\infty}A(n)/n=\lim_{n\to\infty}B(n)/n=c$$ is there anything else that can be said about them necessarily? That is, are there properties that must, or more weakly one should expect to also hold for both sequences?