<p>This study investigated how the physicochemical properties of nontraditional and natural pozzolans (NNPs), including calcined clays, volcanic ashes, fluidized bed combustion ash, and ground bottom ashes, affected the compressive and flexural strengths of concretes prepared with Type I and Type IL cements. By evaluating the impact of NNPs on concrete strength across cement types, this study showcases their potential as alternatives to traditional supplementary cementitious materials (SCMs) that are becoming increasingly scarce and demonstrates that 56&#xa0;days compressive strength can be accurately predicted from the physicochemical properties of NNPs. Results showed that regardless of cement type, concretes containing calcined clays or volcanic ashes showed increased compressive strength compared with plain concrete, with increases of at least 9% and 16% at 28 and 56&#xa0;days. Concretes with fluidized bed combustion ashes or ground bottom ashes showed significant increases in 56&#xa0;days compressive strengths. At 28&#xa0;days, most Type I cement mixtures with NNPs had similar flexural strength to the corresponding plain concrete mixture, and Type IL mixtures with calcined clays and volcanic ashes obtained higher flexural strengths compared to the Type IL reference mixture. The strength improvements were partially attributed to mineralogical characteristics of the NNPs, as higher contents of amorphous and reactive aluminosilicate phases promoted increased formation of C-(A)-S-H. A statistical model based on these physicochemical parameters achieved <i>R</i>² = 0.91 for predicting 56&#xa0;days compressive strength, and the correlation between calcium hydroxide consumption and strength further confirmed the pozzolanic nature of the NNPs and their suitability as SCMs for use in concrete.</p>