In this work, it is studied the convergence of some numerical methods for solving delay differential equation (DDE) with constant delay: y'(t)=f(t,y(t))+g(t,y(t),y(t-\tau)), t >= t_{0}, y(t) = \phi(t), t <= t_{0}. Specifically, we will analyse the stability of linear multistep implicit-explicit (IMEX) methods: \sum_{j=0}^{s} \alpha_{j} y_{n+j}=h\left(\sum_{j=0}^{s}\beta_{j}f(t_{n+j},y_{n+j})+\sum_{j=0}^{s-1}\beta_{j}^{*} g(t_{n+j},y_{n+j}, y_{n+j-m})\right), h being the step size that verifies the constraint h=\tau/(m-u), with m \in \N and 0 <= u <= 1; y_{i}=y(t_{i})=y(t_{0}+ih) the approximation of the state variable, f_{i}=f(t_{i},y_{i}) and g_{i}=g(t_{i},y_{i},y_{i-m}); and \{\alpha _{j},\ \beta _{j}, \ \beta _{j}^{*}\}_{0\leq j \leq s} the coefficients of the method. Convergence is considered a sum of stability plus consistency. It is well-known how to develop high-order numerical methods, but, in the scientific literature, the stability of these methods is usually studied by analyzing the scalar equation y'(t) = \lambda y(t) + \mu y(t-\tau), \quad \lambda, \mu \in \C. However, in this way we reduce the study of stability to systems of DDEs y'(t) = A y(t) + B y(t-\tau), only when A and B are simultaneously diagonizable (and therefore after a transformation it can be analysed through the analysis of d scalar problems). In this work, for several different multistep methods, first, it is analyzed in detail the case where both matrices diagonalize simultaneously, and sufficient and necessary conditions to obtain linear stability are proved. However, it focuses on the case where the matrices A and B are not simultaneously diagonalizable. The concept of field of values, denoted by F(.), is used to prove sufficient conditions for unconditional stability of these methods (i.e. for any step size). Furthermore, sufficient conditions are derived to ensure stability, but according to the step size as a function of the radius of the disk centered at 0 containing F(A^{-1} B) (see [1,2]).