The paper is devoted to a discussion of the properties of electromagnetic waves propagating with a velocity W <c. Boundary conditions are obtained for structures with very narrow slots, either closed or open, and a general method of solution of the wave equations is discussed. Fields in the free region and in the slot region are expanded in convenient Fourier series and these series joined along the border of both regions. In doing this, it can be proved that the field contains a dominant term, completed by corrections that represent the field distortion near the open end of the slots. Under favorable conditions, and for very narrow slots, the dominant terms are by far the most important. This allows for a simplified discussion of a variety of examples. The results obtained are in agreement with those of E. L. Chu and W. W. Hansen (J. App. Phys. 18, 996 (1947)).