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Surface waves in homogeneous absorbing layers are studied. The transformation of surface waves into other types of guided waves with frequency or layer's parameters variations is analyzed. It is found that in absorbing layers the standing damped surface waves do not exist and continuous transformation of surface waves into leaky waves is forbidden. Surface waves can only transform continuously into nonphysical waves with field strengths increasing exponentially in both the direction of propagation and in normal direction away from the layer into free-space. The frequency at which surface waves transform into nonphysical waves can be considered as cutoff frequency of surface waves. New and more general definitions previously proposed by the authors for the phase and energy velocities of guided waves are analyzed. It is shown that these velocities are identically equal to each other and never exceed the lightspeed in free-space. Several new physical phenomena are discovered. These are the upper frequency cutoff, its shifting to higher frequencies for materials with lower losses and the merging of high TE wave modes.