The insects which are both forward and back ward running habit

The insects which are both forward and backward running habit Embioptera.
The name Embioptera ("lively wings") comes from Greek (embios), meaning "lively", and (pteron), meaning "wing", a name that has not been considered to be particularly descriptive for this group of fliers, perhaps instead referring to their remarkable speed of movement both forward and backward.
On landing, these chambers deflate and the wings become flexible, folding back against the body. Wings can also fold forwards over the body, and this, along with the flexibility allows easy movement through the narrow silk galleries, either forwards or backwards, without resulting in damage.