EN EL PRESENTE ARTÍCULO SE ESTUDIA LA RESONANCIA PRINCIPAL GENERALIZADA PARA SISTEMAS DESCRITOS POR ECUACIONES DIFERENCIALES ORDINARIAS DE SEGUNDO ORDEN Y SE DEMUESTRA CON AYUDA DEL PRINCIPIO DEL MÁXIMO DE PONTRIAGUIN, LA COINCIDENCIA DE ESTA CON LA SOLUCIÓN PROLONGADA DE UN PROBLEMA EXTREMAL PARA EL MISMO SISTEMA. ADEMÁS SE VERIFICA ESTOS RESULTADOS EN LOS CASOS PARTICULARES DE RESONANCIA GENERAL Y RESONANCIA PARAMÉTRICA PARA LA ECUACIÓN DE MATHIEU.AbstractTHIS PAPER WILL DESCRIBED THE GENERALIZED PRINCIPAL RESONANCE OF SYSTEMS AS DESCRIBED BY THE SECOND ORDER OF ORDINARY DIFFERENTIAL EQUATIONS AND PROVED BY THE PONTRIAGUIN MAXIMAL PRINCIPLE TO COINCIDE WITH THE LENGTHENED SOLUTION OF AN EXTERNAL PROBLEM OF THE SAME SYSTEM. TEH RESULTS ARE VERIFIED IN SPECIAL CASES OF GENERAL RESONANCE AND PARAMETRIC RESONANCE FOR THE MATHIEU EQUATION.THIS PAPER WILL DESCRIBED THE GENERALIZED PRINCIPAL RESONANCE OF SYSTEMS AS DESCRIBED BY THE SECOND ORDER OF ORDINARY DIFFERENTIAL EQUATIONS AND PROVED BY THE PONTRIAGUIN MAXIMAL PRINCIPLE TO COINCIDE WITH THE LENGTHENED SOLUTION OF AN EXTERNAL PROBLEM OF THE SAME SYSTEM. TEH RESULTS ARE VERIFIED IN SPECIAL CASES OF GENERAL RESONANCE AND PARAMETRIC RESONANCE FOR THE MATHIEU EQUATION.