The existence of the second (according to the module) eigenvalueλ2of a completely continuous nonnegative operatorAis proved under the conditions thatAacts in the spaceLp(Ω)orC(Ω)and its exterior squareA∧Ais also nonnegative. For the case when the operatorsAandA∧Aare indecomposable, the simplicity of the first and second eigenvalues is proved, and the interrelation between the indices of imprimitivity ofAandA∧Ais examined. For the case whenAandA∧Aare primitive, the difference (according to the module) ofλ1andλ2from each other and from other eigenvalues is proved.
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