There are provided a waveform observing apparatus and waveform observing system that solve a problem of displacement of a handwritten comment which occurs with enlargement/reduction in display in such a manner that, when a determination is NO in a process step, namely when a current compression ratio differs from a compression ratio at the time of writing a handwritten comment in displaying the handwritten comment to such a degree as to cause occurrence of non-allowable displacement, a process proceeds to a next process step, and a simple indication indicating the presence of the handwritten comment is displayed in a position associated with a portion of a waveform corresponding to a measured data number.