In this paper, we study the electromagnetic response of a cold plasma with dissipation ν > 0 in a general slab geometry (plasma density n 0 (x) and background magnetic field B 0 (x) e 3). We express the behavior of the electromagnetic field (E, H) (at a given frequency ω) in the neighborhood of the hybrid resonance x h solution of ω = ω h (x). This generalizes to any incident wave vector (k 1 , k 2 , k 3) the result obtained by Després, Imbert-Gérard and Lafitte in the normal incidence case (the incoming electromagnetic field has its wave vector belonging to the orthogonal plane to e 3 , i.e., k 3 = 0), hence treating a fully coupled system of ODEs of order 4. This is done by deducing from the complete system of ODEs an integro-differential system whose differential part contains a regular singular point at ν → 0 +. This new system is then solved in the neighborhood of this regular singular point by using the variation of parameters method. In the oblique incidence case at the limit ν → 0 + , we observe that (E 2 , E 3 , H 2 , H 3) are integrable in the neighborhood of x h uniformly in ν → 0 + , while the most singular term of the limit of ε 0 E 1 when ν → 0 + is proportional to P .V. 1 x − x h − iπ sign(∂ x ω h (x h))δ x h + a ln(x − x h) + .