The authors consider linear systems with uncertainty and time delay that are described by the equations of the following type: $$\dot x(t)=Ax(t)+B_0x(t-\tau_0)+\sum_{j=1}^r\beta_j B_jx(t-\tau_j).$$ Here: \begin{itemize} \item The uncertainty in a matrix $A$ is caused by $m$ unknown factors $\alpha_i$: $A=A_0+\alpha_1A_1+...+\alpha_m A_m$; the matrices $A_i$ (that describe the dependence of $A$ on these factors) are known; the values of the factors $\alpha_i$ are unknown, but we know the bounds $\mu_i$ for these values: $\alpha_i\in [-\mu_i,\mu_i]$. \item The coefficients $\beta_j$ at the "unwanted" delay terms are unknown; we know the bounds $\nu_j$ for these coefficients ($\beta_j\in [-\nu_j,\nu_j]$), and we know the matrices $B_j$ that describe the influence of these delays on the system. \item The values of the delays $\tau_k$ are unknown. \end{itemize} Based on the available information, we want to find out whether the system is stable or not; to be more precise, whether the system is guaranteed to be stable (i.e., is {\it robustly stable}), or it may not be stable for some possible values of the unknown parameters $\alpha_i$, $\beta_j$, and $\tau_k$. The authors describe new sufficient criteria for robust stability of such systems.