  Weanalyzethecomputationalcomplexityofanalgorithmtosolve the conjugacy search
problem in a certain family of metabelian groups. We prove that in general the
time complexity of the conjugacy search problem for these groups is at most
exponential. For a subfamily of groups we prove that the conjugacy search
problem is polynomial. We also show that for a different subfamily the
conjugacy search problem reduces to the discrete logarithm problem.
