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Abnormal velocities in passive structures such as one-dimensional (1-D) photonic crystals and a slab having a negative index of refraction are discussed. In the case of 1-D photonic crystal, the frequency- and time-domain experiments for waves tuned to the bandgap of the photonic crystal demonstrate a positive group velocity exceeding the speed of light in vacuum (superluminal). In the case of a medium with negative index of refraction, our theoretical studies show that such a medium can support positive group and negative phase velocities (backward waves), as well as negative group and negative phase velocities. The meaning of superluminal group velocity and negative group velocity, or equally, positive superluminal group delay and negative group delay, are discussed. It is shown that despite their counterintuitive meaning there are no contradictions with the requirements of relativistic causality (Einstein causality). To clearly demonstrate this, the important subject of the "front" is reintroduced.