Numerous field observations show that most water flow in fractured rocks takes place in only a small part of the fractures. We call these channels. Solutes in the flowing water can diffuse in and out of stagnant water in the porous rock matrix that the flowing water contacts via the so-called flow wetted surface (FWS). In addition, the solutes can diffuse into stagnant water in the fractures themselves and from this water further into the rock matrix. For narrow channels with small FWS the transport via the stagnant water in the fracture can considerably add to the exchange of solutes between flowing water and matrix water. For sorbing solutes that interact with the micropore surfaces in the matrix the effect can be very strong. Some models that account for these processes are developed and solved using Laplace transforms. Some examples are presented that show the effects of first diffusion into stagnant waters in fractures with subsequent diffusion into the rock matrix. Effects of slit-like and tube-like channels are considered as well as the presence of intersecting fractures. The solutions are especially useful to model solute transport in complex three-dimensional channels networks where wide and narrow or even tube-like channels with widely varying flow rates combine into a multitude of different paths.