Context. Short-period high-amplitude pulsating stars of Population I (delta Sct stars) and II (SX Phe variables) exist in the lower part of the classical (Cepheid) instability strip. Most of them have very simple pulsational behaviours, only one or two radial modes being excited. Nevertheless, BL Cam is a unique object among them, being an extreme metal-deficient field high-amplitude SX Phe variable with a large number of frequencies. Based on a frequency analysis, a pulsational interpretation was previously given. Aims. We attempt to interpret the long-term behaviour of the residuals that were not taken into account in the previous Observed-Calculated (O-C) short-term analyses. Methods. An investigation of the O-C times has been carried out, using a data set based on the previous published times of light maxima, largely enriched by those obtained during an intensive multisite photometric campaign of BL Cam lasting several months. Results. In addition to a positive (161 +/- 3) x 10(-9) yr(-1) secular relative increase in the main pulsation period of BL Cam, we detected in the O-C data short- (144.2 d) and long-term (similar to 3400 d) variations, both incompatible with a scenario of stellar evolution. Conclusions. Interpreted as a light travel-time effect, the short- term O-C variation is indicative of a massive stellar component (0.46 to 1 M(circle dot)) with a short period orbit (144.2 d), within a distance of 0.7 AU from the primary. More observations are needed to confirm the long-term O-C variations: if they were also to be caused by a light travel-time effect, they could be interpreted in terms of a third component, in this case probably a brown dwarf star (>= 0.03 M(circle dot)), orbiting in similar to 3400 d at a distance of 4.5 AU from the primary.