We study effects on magnetotransport produced by changing the size of the trivalent ions R³⁺ in the layered polycrystalline materials Sr₂RMn₂O₇ (R = Pr,Nd,Ho,Y) and by varying the mixed-valence ratio Mn³⁺/Mn⁴⁺ in the series Sr_2-xNd_1+xMn₂O₇ (x = 0,0.1,0.2,0.5). The results of our magnetic and electrical measurements are related to the measured structural characteristics of each compound. For the Sr₂RMn₂O₇ series, colossal magnetoresistance (CMR) is observed below 150 K for R = Pr and R = Nd but not for samples containing R = Ho or R = Y ions, which have smaller ionic radii. For R = Ho and R = Y, the absence of CMR is correlated with the paramagnetic and insulating properties of the samples. Within the series Sr_2-xNd_1+xMn₂O₇, the CMR effect is also observed for temperatures below 150 K and increases as the temperature decreases. In this series the samples show a mixture of spin-glass and antiferromagnetic behaviour (x = 0,0.1) or no long-range magnetic order (x = 0.2,0.5). The largest CMR at high temperatures (above 100 K) and high magnetic fields (14 T) is observed for the x = 0.2 sample, which also shows the largest magnetization per formula unit. The observed CMR in the compounds studied here is attributed to magnetic cluster formation.