This paper focuses on the analysis and design of families of interval observers for linear systems with a pointwise delay. First, it is proved that classical interval observers for systems without delays are not robust with respect to the presence of delays, no matter how small delays are. Next, it is shown that, in general, for linear systems with delay, the classical interval observers endowed with a pointwise delay are unstable. A new type of design of interval observers enabling circumvention of these obstacles is proposed. It provides framers that incorporate distributed delay terms. The proposed interval observers are assessed through a nonlinear biotechnological model.