This paper focuses on the analysis of some classes of observers for linear systems with a point-wise delay. First, it is pointed out that, classical interval observers for systems without delays are not robust with respect to the presence of delays that appear in a specific structure location, no matter how small it is. Next, it is shown that, in general, for linear systems classical interval observers endowed with a point-wise delay are unstable. A new type of design enabling to circumvent this obstacle is proposed. It relies on framers that incorporate distributed delay terms.