The authors use the generalized Riccati transformation in order to obtain sufficient conditions for an oscillation of the solutions to the following neutral partial differential-functional equations \[ {\partial \over \partial t}\left[p(t) {\partial\over\partial t}\left(u(x,t)+ \sum^\ell_{i=1} \lambda_i(t) u(x,t-\tau_i) \right)\right] = \] \[ =a(t)\Delta u(x,t)+\sum^s_{k=1} a_k(t)\Delta u\bigl(x,t- \rho_k(t)\bigr) -q(x,t)u(x,t)- \] \[ -\sum^m_{j=1}q_j (x,t)f_j \bigl(u(x,t -\sigma_j)\bigr), \quad(x,t)\in\Omega \times [0,\infty), \] with boundary conditions of mixed type or Dirichlet type.