We present randomized approximation algorithms for multi-criteria Max-TSP. For Max-STSP with
k > 1 objective functions, we obtain an approximation ratio of
\frac 1k - e\frac 1k - \varepsilon
for arbitrarily small
ε> 0. For Max-ATSP with
k objective functions, we obtain a ratio of
\frac1k+1 - e\frac{1}{k+1} - \varepsilon
.