A Ramanujan pair consists of two sequences \(\{a_ n\}\) and \(\{b_ n\}\) of positive integers such that \[ \prod_{n\geq 1}(1-q^{a_ n})^{- 1}=1+\sum_{n\geq 1}\frac{q^{b_ 1+b_ 2+...+b_ n}}{(1-q)(1-q^ 2)...(1-q^ n)}. \] A number of Ramanujan pairs can be found among the classical partition identities and their are ten known examples. This paper deals with analytic rather than combinatorial consequences of the above identity. Asymptotic formulae are obtained for the coefficients in the power series expansion of the two sides of the identity for certain ''regular'' sequences defined in the paper. A comparison of these asymptotic formulae leads to severe restrictions on the sequences in a Ramanujan pair and the identity cannot hold for regular sequences with \(a_ n\sim b_ n\) as \(n\to \infty\) except possibly in one special case. The analysis depends on ideas developed by Szekeres. Other partition identities have been treated in a similar way by Richmond, Szekeres and Loxton, the asymptotic analysis of partition identities can be used to derive identities for the dilogarithm function \(Li_ 2(z)=\sum^{\infty}_{n=1}z^ n/n^ 2\). The known Ramanujan pairs correspond in this way to evaluations of the dilogarithm function at certain algebraic points.