Bronchial diseases are characterised by the weak efficiency of mucus transport through the lower airways, leading in some cases to the muco-obstruction of bronchi. It has been hypothesised that this loss of clearance results from alterations in the mucus rheology, which are reflected in sputum samples collected from patients, making sputum rheology a possible biophysical marker of these diseases and their evolution. However, previous rheological studies have focused on quasi-static viscoelastic (linear storage and loss moduli) properties only, which are not representative of the mucus mobilisation within the respiratory tract. In this paper, we extend this approach further, by analysing both quasi-static and some dynamic (flow point) properties, to assess their usability and relative performance in characterising several chronic bronchial diseases (asthma, chronic obstructive pulmonary disease, and cystic fibrosis) and distinguishing them from healthy subjects. We demonstrate that pathologies influence substantially the linear and flow properties. Linear moduli are weakly condition-specific and even though the corresponding ranges overlap, distinct levels can be identified. This directly relates to the specific mucus structure in each case. In contrast, the flow point is found to strongly increase in muco-obstructive diseases, which may reflect the complete failure of mucociliary clearance causing episodic obstructions. These results suggest that the analysis of quasi-static and dynamic regimes in sputum rheology is in fact useful as these regimes provide complementary markers of chronic bronchial diseases.