The non-linear order $M<\int$ of the Markov process $\{X(t),\ 0\leq t\}$ is defined as $M=\sup_sM(s)$ where $M(s)$ is the minimal number of random variables generating $\sigma\{E_sX(t),\ s\leq t\}$ ($E_s(\cdot)$ is the conditional expectation with respect to $\sigma\{X(u),\ u\leq t\}$). The relation between the non-linear and linear order of the Markov process is discussed. The latter is a modification of the Hida multiple Markov process.