They are rapidly broken down in cells (to terminate the signal) by enzymes called phosphodiesterases.
We know that phosphodiesterases are important in tubules because the response to cyclic nucleotides is enhanced by phosphodiesterase inhibitors, such as IBMX or (in the case of cGMP) Zaprinast.
References
Dow, J. A. T., Maddrell, S. H. P., Davies, S.-A., Skaer, N. J. V. and Kaiser, K. (1994). A novel role for the nitric oxide/cyclic GMP signalling pathway: the control of fluid secretion in Drosophila. Am. J. Physiol. 266, R1716-R1719. (Medline 94262936)