We report the observation of fractional echoes in a double-pulse excited nonlinear syst em . Unlike standard echoes which appear p eriodically at delays which are integer multiple of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide the first experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of C02 molecules excited by a pair of femtosecond laser pulses . 37.10.Vz, 42. 50. Md Many nonlinear syst ems display the phenomenon of echoes, which is a series of delayed impulsive responses after a pair of short external pulses . These echoes typ-· icany show themselves at times T rv T , 2T, 3T, etc. after the end of the excitation, where T is the delay between the stimulating pulses . Echoes are common in many ar-· eas of physics, including NMR [1] , plasma physics [2--4], nonlinear optics [5], cavity quantum electrodynam-· ics [6 , 7], and cold atoms physics [8][9][10][11] . Echoes were predict ed to occur in proton storage rings [12 , 13], and were observed in high energy hadron b eam experiments [14,15] . Echo-enabled generation of short-wavelength ra-· diation in free-electron lasers [16][17][18] was demonstrat ed (for a recent review, see [19]) .Recently we reported the exist ence of orienta-· tion/ alignment echoes in an ensemble of free classi-· cal rotors stimulat ed by an external impulsive force [20] . We attributed t he echo formation to the kick-· induced filamentation of the rotational ph ase space, and demonstrated the effect experimentally in a gas of C0 2 molecules excited by a pair of femtosecond laser pulses. The time-dependent mean molecular alignment (defined as (cos 2 (B) )(t) , where e is the angle between t he molec-· ular axis and laser polarization) was measured via the laser-induced birefringence signaL The excited syst em exhibited a regular sequence of echo pulses at delays T = T , 2T, 3T, . . . . In addition, our theoretical analysis and numerical simulations [20] also predict ed unusual ad-· ditional recurrences (fractional echoes) at T = (p j q)T, where p and q are mutuany prime numbers. These frac-· tional echoes, however cannot be seen in the alignment signal -t hey require measurement of higher order mo-· ments of the molecular angular distribution.Here we present the first observation of the phe-· nomenon of fractional echoes measured via third-· harmonic generation (THG) in a gas of C0 2 molecules at room t emperature and pressure of 80 mbar. In what follows we introduce the mechanism of the fractional echoes by using a simple 2D classical model, and then describe our experiments in which t he phenomenon of fractional echoes was observed . We also compare the experimental result s to the fun three-dimensional classical and quantum simulations of the echo formation .For a nonresonant laser field interacting with a symmetric linear molecule, such as N 2 , 0 2 or C0 2 , the angular-dependent interaction potent...