The waiting spectra of the sets consisting of pairs of sequences with prescribed quantitative waiting time indicators are determined. More precisely, let $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{R} (x,y)$$ and $$\bar R(x,y)$$ be the lower and upper quantitative waiting time indicators of y by x respectively in the symbolic space Σ m (integer m ⩾ 2) and define the level sets $$S_{\alpha ,\beta } = \left\{ {(x,y) \in \Sigma _m^2 :\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{R} (x,y) = \alpha ,\bar R(x,y) = \beta } \right\},$$ where 0 ⩽ α ⩽ β ⩽ ∞, it is shown that the sets S α,β are all of Hausdorff dimension 2. Besides, some further extensions of this result are also made.