Laser initiation of energetic materials is a topic of significant interest. An extremely important parameter of initiation for numerous applied tasks is the time delay of initiation from the beginning of laser exposure. Experimental studies of the process of initiation of a number of primary explosives (lead styphnate (LS), lead azide, (LA)) and initiating mixtures (potassium perchlorate and potassium hexacyanoferrate (III) (PP/PH), bismuth oxide and aluminum - nanothermite (NT)) under the exposure of a continuous IR (0.915 mu m) laser with a power of up to 10 W were carried out. The time delay of initiation of these explosives was measured. It is shown that nanothermite (NT) has the lowest time delays and minimal initiation thresholds. At a laser power of 1 W and a light spot diameter of 0.5 mm (intensity 0.5 kW / cm(2)) the time delay of NT initiation was 1.2-1.8 ms. For other explosives with such a laser spot diameter, the initiation threshold was 2-3 W (1-1.5 kW/cm(2)). It is shown that mixtures of these explosives photosensitized by 0.5 % nanoaluminum have an initiation threshold ten times lower than for pure materials. For such compositions, the initiation time delay was 2-10 ms at the laser radiation intensity of 0.5 kW/cm(2). It was found that for the PP/PH material there is a certain limit on the minimum time delay of initiation, which was 0.1-0.15 ms. It is suggested that this effect is associated with the micro-hotspot nature of laser initiation of EM and the presence of a critical zone of initiation.