Let u = {u(t, x) ; t ∈ [0, T ], x ∈ R d } be the process solution of the stochastic heat equation u t = ∆u +Ḟ , u(0, ·) = 0 driven by a Gaussian noisė F , which is white in time and has spatial covariance induced by the kernel f . In this paper we prove that the process u is locally germ Markov, if f is the Bessel kernel of order α = 2k, k ∈ N + , or f is the Riesz kernel of order α = 4k, k ∈ N + .