Given a sequence of district real numbers \(\Lambda= (\lambda_j)^\infty_{j=0}\), the elements of the linear span \(M_n(\Lambda)\) of \(\{x^{ \lambda_0}, x^{\lambda_1}, \dots,x^{\lambda_n}\}\) are called Müntz polynomials (with respect to \(\Lambda)\). The author proves several variants of Markov-type inequalities for products of Müntz polynomials. The main result reads as follows: For increasing sequences \(\Lambda=(\lambda_j)\) and \(\Gamma=(\gamma_j)\) let \[ K\bigl(M_n (\Lambda),M_n (\Gamma)\bigr): =\sup\left\{ {\bigl \|x(pq)'(x) \bigr\|_{[0,1]} \over\|pq\|_{[0,1]}}:p\in M_n (\Lambda), q\in M_n(\Gamma) \right\}. \] Then \[ \begin{aligned} {1\over 3}\bigl((m+1)^{ \lambda_n}+ (n+1)\gamma_m\bigr) & \leq K\bigl(M_n(\Lambda),M_n(\Gamma)\bigr)\\ & \leq 18(n+m+1)(\lambda_n+\gamma_m),\end{aligned} \] which implies in particular \[ {2 \over 3}(n+1)\lambda_n\leq K\bigl(M_n (\Lambda),M_n(\Lambda) \bigr)\leq 36(2n+1) \lambda_n. \] Under some extra assumptions, variants are given with \(x\) dropped, and with \([0,1]\) replaced by \([a,b] \subset(0,\infty)\).